Eleven days in Serbia, North Macedonia and Greece: the corridor everybody flies over

Go straight to the point of the ridge. The fortress park at the western end of the old town covers the whole promontory where the Sava meets the Danube, and it is free, open and full of people at any hour. There has been a fort here since the Romans put a legionary camp on it, and the walls you walk on are largely Austrian and Ottoman work of the seventeenth and eighteenth centuries, laid over medieval Serbian and Hungarian layers.

The view from the upper terrace is the reason the city exists. Two large rivers meeting at right angles, the flat Pannonian plain running away north, and the tower blocks of the postwar new town on the far bank. Come back at sunset if the light is good.

Walking back into town, the cathedral on the edge of the old quarter went up between 1837 and 1840, in a plain neoclassical shell with a spectacularly gilded iconostasis inside and the tombs of two Serbian princes. It takes fifteen minutes and it is the best surviving building of the period when Serbia was inventing itself as a state.

Then eat. The old bohemian street of taverns north of the main square has been trading on its reputation since the 1890s, and it is touristy and still good: grilled meat, live music that will not let you talk, and a bill that will not hurt.

Start with the small museum devoted to the engineer who worked out how to send electricity over long distances. It holds his papers, his instruments, working models you are allowed to switch on, and, in a gilded sphere on a plinth, his ashes. He was born in what is now Croatia, lived his working life in New York and never set foot in this building, which does not stop the city treating him as its own.

Ten minutes uphill is one of the largest Orthodox churches in the world, begun in 1935 on the spot where an Ottoman grand vizier is said to have burned the relics of the Serbian church's founding saint in 1595. Work stopped for the war, stopped again for most of the communist period and only finished inside a few years ago. The mosaic in the dome covers thousands of square metres and is best seen from the crypt stairs, which is also where the acoustics are.

In the afternoon, take a bus out to the museum complex on the hill in the diplomatic quarter, where Josip Broz Tito is buried in a glasshouse he used as a winter garden. Around the grave are the relay batons carried across Yugoslavia every year for his birthday, thousands of them, each designed by a different factory or school, and the effect is somewhere between touching and very strange.

The rest of the museum covers the country that no longer exists, without much editorialising, and the gap between the confidence of the objects and what happened next is the whole exhibit.

Three hours down the motorway through the Morava valley, which is Serbia's spine and has been the invasion route into and out of the Balkans since antiquity. Coaches leave through the day and the ride is dull, which is the only dull thing on this route.

Nis was Naissus, a Roman town on the road to Constantinople, and Constantine the Great was born here in about 272. The remains of a fourth century imperial villa complex sit four kilometres east on the Sofia road, with mosaic floors under cover, a water tower, granaries and the outline of a palace. It is modest by Roman standards and it is the direct physical connection to the man who moved the empire's capital and its religion.

Back in town, the fortress on the north bank of the river is Ottoman work of the 1720s built straight over the Roman street grid, with the main gate, the walls and a mosque still standing. Inside it is a park, and half the city is in it on a warm evening.

The third site is a small chapel on the eastern edge of the centre, built around a tower. In 1809 a Serbian commander losing the battle on the hill outside town fired into his own powder store rather than surrender. The Ottoman commander had the dead beheaded and their skulls mortared into a tower beside the road as a warning. Fifty-odd remain of the original nine hundred and fifty. It takes ten minutes to see and rather longer to stop thinking about.

Four hours south with a passport check at the border, where the coach empties and everybody stands about while the stamps are done. The valley narrows after Vranje and you cross into North Macedonia through hills that were the frontier of the Ottoman Empire for a very long time.

Skopje's main square is the place to start, because it explains the rest. In the middle of it stands an enormous bronze horseman on a column in a fountain, officially titled Warrior on a Horse and understood by everybody to be Alexander the Great. It went up in 2011, at the height of a government programme that added several hundred statues, a triumphal arch and a great deal of neoclassical cladding to a city centre that had been rebuilt in modernist concrete after the earthquake.

Walk north across the bridge. The stone arches under your feet are the real thing, on Roman foundations and rebuilt in the fifteenth century, and they have been the crossing point for six hundred years. On the far side the marble stops and the Ottoman city begins in about four paces.

The bazaar above the bridge is one of the largest surviving in the Balkans: a hill of narrow lanes, mosques, tea shops, jewellers and grill houses, still functioning as a market rather than a museum. Eat here. It is cheap, it is excellent, and it stays busy until late.

Start uphill in the bazaar at the mosque on the terrace, built in 1492 by an Ottoman governor and the finest Islamic building in the country: a single great dome, a courtyard with a fountain and a rose garden, and a view down over the roofs of the market. It is open to visitors outside prayer times and the caretakers are used to them.

Above it, the fortress walls run along the top of the ridge. Little of the interior survives beyond archaeology and a lot of grass, but the walk along the ramparts is the best way to see how the city is arranged: the bazaar tumbling down one side, the river, the marble quarter beyond it and the mountain closing the view to the south.

In the afternoon, come down to the memorial centre on the south bank, built on the site of the Jewish quarter that was cleared to make room for it. In March 1943 the Bulgarian occupying authorities rounded up 7,144 Jews from Macedonia and handed them to the Germans; almost all were murdered at Treblinka within weeks, and something like ninety-eight per cent of the community did not survive the war. The museum is thorough, modern and very quiet.

Afterwards, go back over the river and sit in the bazaar with a tea. It is the right way to end a day like that, and it is also where the city is most itself.

The best road leg of the trip. The coach follows the Vardar south through a gorge, out through the second border and onto the plain that Alexander's father ruled from a palace an hour west of where you are going. Four hours, one passport check, and the language changes alphabet again on the far side.

Thessaloniki gives you Roman first. The emperor Galerius built himself a palace quarter here around the year 300, and three pieces of it survive in the middle of the modern grid: a triumphal arch straddling what is still the main street, a domed rotunda, and the foundations of the palace itself under a square.

The arch went up in 303 to celebrate a victory over the Persians and the surviving piers are carved from top to bottom with the campaign, in registers, like a comic strip. It is free, unfenced and people walk their dogs past it.

Two minutes north is the rotunda, a brick drum built as part of the same complex and almost as old as the Pantheon in Rome, which it resembles. It has been a temple, a church with extraordinary gold mosaics still in the vault, and a mosque, and the minaret from the last of those is still standing outside.

End at the water. The white tower on the seafront is Ottoman, about thirty-four metres high, and was for a long time a prison notorious enough to be called the tower of blood. It is now a museum of the city with a spiral ramp to the roof, and the roof at sunset is where Thessaloniki goes.

Begin at the basilica of the city's patron, a vast five-aisled church of the seventh century raised over the Roman baths where a young officer was killed for his faith in about 306. The building burned in the great fire of 1917 and was rebuilt from its own foundations by 1949, so what you see is honest reconstruction around genuine columns and a handful of surviving mosaic panels.

The crypt is the reason to come, and most visitors miss it: the stairs are to the right of the altar. Underneath is the Roman bath structure itself, with a fountain, marble fragments and the shrine that the whole enormous church was built to cover.

Ten minutes west, the Roman forum sits in a hollow below street level, complete with an odeon, a cryptoporticus and a small museum in the vaults underneath. It was found by accident in the 1960s when the ground was cleared for a courthouse, which was then built somewhere else.

Spend the afternoon at the museum of Byzantine culture out towards the exhibition grounds. It is arranged as a walk through a thousand years, from early Christian house churches through icons, tomb paintings, jewellery and coins to the fall of Constantinople, and it is exceptionally well laid out.

Then dinner, and take it seriously. The lanes around the covered market are full of small ouzeries where you order six or seven plates between two and stay until the place shuts.

The train south is the easiest travel day of the trip and the most scenic: a modern intercity service doing just over four hours, with Mount Olympus on the right, out across the Thessalian plain and down into Attica. Reserve a seat, bring a coffee and watch Greece go past.

Athens gives you a soft landing. Walk down from the square in front of parliament in the late afternoon and take the arch first, a marble gateway put up around 131 to mark where the old Greek city ended and the emperor Hadrian's new quarter began. There are inscriptions on both faces saying exactly that, one on each side, which is a piece of Roman cheek worth reading in the original.

Behind it stand the columns of what was, when it was finished, the largest temple in Greece. It was begun in the sixth century BC by a tyrant, abandoned unfinished for six hundred and fifty years, and completed by Hadrian in the same building campaign as the arch. Fifteen of its hundred and four columns are standing; one more lies where a storm dropped it in 1852, in sections, like a stack of coins.

That is enough for an arrival day. Walk back up towards the parliament for the changing of the guard on the hour, which is performed in pleated skirts and pom-pom shoes at a pace that has to be seen, and then find dinner in the streets below.

Be at the gate when it opens. In summer that is eight, the site is at its busiest between ten and one, and the rock has almost no shade. The main entrance on the west side takes the coach parties; the smaller gate on the south side, by the museum, usually has a shorter line.

The climb goes up through a monumental marble gatehouse and out onto the plateau, and the effect at the top is not the temple so much as the space: a flat rock the size of a few football pitches, standing clear above a city of three million, with mountains on three sides and the sea on the fourth.

The great temple was built in fifteen years in the middle of the fifth century BC, out of marble quarried sixteen kilometres away, and it survived nearly intact as a church and then a mosque until a Venetian shell hit the Ottoman powder store inside it in 1687 and blew the middle out. Everything you see being done to it now is a slow, exacting reassembly that has been running since 1975.

Do not miss the smaller temple on the north edge, the one with six draped women standing in for columns on its southern porch. Those are copies; five of the originals are in the museum below and the sixth is in London.

Then go down to that museum. It is built over an excavated neighbourhood you walk across on glass, and its top floor is a glass gallery the exact size and orientation of the temple above, holding the surviving sculpture in the order it was carved. Standing there with the real thing framed in the window is the best hour in Athens.

The ancient civic centre lies on the low ground north-west of the rock, and it is the part of Athens where the interesting things actually happened: the law courts, the mint, the council house, the shops and the covered walks where Socrates went to annoy people. Today it is a green archaeological park full of tortoises and it takes a comfortable two hours.

The temple on the western rise is the best preserved Greek temple anywhere, largely because it spent thirteen hundred years as a church. It is fifth century BC, Doric, and it has its roof, which nothing else of that age does. Nobody photographs it because it is not on the skyline.

The long two-storey building on the eastern edge is a full reconstruction from the 1950s of a second century BC shopping arcade, built on the original foundations with the original materials where they survived. It houses the site museum, and it is the only way to walk through an ancient Greek building rather than around one.

Give the afternoon to the national archaeological collection, twenty minutes north of the centre. It is the best museum of Greek antiquity in the world and it is arranged chronologically, which means you can walk from Cycladic figurines through the gold from the Mycenaean shaft graves to classical bronzes in an hour if you are firm with yourself. The bronze of a god throwing something, recovered from a shipwreck, and the corroded geared calculator recovered from another one, are both here.

Finish in the old quarter under the north slope of the rock, which is where everybody eats, and accept that it is touristy.

One last thing, and it is a good one. The stadium in the hollow behind the parliament gardens was cut into the hillside in the fourth century BC, rebuilt in marble by a rich Athenian in the second century AD, and then excavated and rebuilt in marble again for the first modern Olympic Games in 1896.

It seats about fifty thousand on stone benches and it is the only stadium in the world built entirely of marble. The audio guide is included, the tunnel the athletes used still runs under the far end, and you can sit in the emperor's throne and run on the track. It takes an hour and it is a much better last morning than another museum.

The airport is forty minutes out on the metro from the square in front of parliament, with a flat fare and departures every half hour, and the same line runs to the port at Piraeus in the other direction if you are carrying on to the islands.

If the flight is late, the hill with the pines gives you the Acropolis one more time for nothing, and it is ten minutes from the stadium by taxi.