Six days in Bosnia and Herzegovina: two towns joined by the best short train ride in Europe

Start in the middle of the bazaar, at the wooden drinking fountain on the pigeon square. It was built in 1753 and moved to this spot in 1891 by an Austrian architect who liked it enough to keep it, which is the history of this city in one object. The water is drinkable and the local line is that whoever drinks it comes back.

The lanes around it are still organised by trade, as they have been since the fifteenth century: coppersmiths hammering shell casings into coffee pots in one street, gold in the next, leather in a third.

The great mosque is a minute west. Gazi Husrev-beg was the Ottoman governor who effectively built Sarajevo, and his mosque of 1531 is the finest classical Ottoman building outside Turkey, with a domed prayer hall, a courtyard fountain and his tomb in the graveyard. It was deliberately shelled in the 1990s and reopened in 2002. Cover shoulders and knees; scarves are provided at the door.

Then a small museum in a domed silk market of 1551, which lays out the whole story of the place from the Romans onwards around a model of the Ottoman town. Afterwards, coffee in the courtyard of the only surviving caravanserai, which has been serving travellers on this spot since 1551 and still does.

Dinner is cevapi. There is no alternative on a first night here and you would not want one.

There is a line set into the pavement on Ferhadija street reading Sarajevo Meeting of Cultures, and it is not an invention of the tourist board. Look east and you see a sixteenth century Ottoman bazaar; turn round and you are looking down a Viennese shopping street. The empire changed in 1878 and the builders simply carried on from where the old town stopped.

Four buildings this morning, all within a few minutes of that line. The Old Orthodox Church is the oldest, first recorded in 1539 and built half-sunken into the ground because non-Muslim buildings were not permitted to rise above their neighbours; inside it is dark carved wood and gilt, with an icon museum upstairs.

Five minutes away, the Old Temple of 1581 was built for Sephardic Jews who came here after the expulsion from Spain and made this one of the great Sephardic cities of Europe. It is the Jewish museum now, and it tells four good centuries before the floor that deals with 1941.

Then the Catholic cathedral, neo-Gothic, begun in 1884, with a pockmarked square in front where shell craters have been filled with red resin. Sarajevo has hundreds of these roses in its pavements and once you have noticed one you cannot stop.

In the evening go up the twisted glass tower west of the centre, which has a bar on the thirty fifth floor and an open deck two floors above it. From up there the shape of the valley, and the ring of hills around it, makes immediate and uncomfortable sense.

This is the hard day and it is best done in one go.

By 1993 the city was completely encircled. The airport was in United Nations hands and could not be crossed, so two teams dug towards each other from houses on either side of the runway and met in the middle. The result was 800 metres long, about a metre and a half high, unlit and often flooded, and for the rest of the siege it was the only way in or out of Sarajevo. Food, fuel, weapons, wounded people and the president all went through it bent double. Twenty five metres survive under the house at the far end, with the trolleys and the wooden props.

The road back into town is the one that was called Sniper Alley: a long straight boulevard overlooked from the ridges, which people crossed at a run for four years while the international press watched from a hotel halfway along.

In the afternoon, the museum that collects ordinary objects belonging to people who were children under the siege, each with a few sentences written by the person who kept it. A shoe, a diary, a violin. It sounds slight and it is the most powerful room in the country.

Finish at the city hall by the river, the striped Moorish building at the mouth of the gorge, built by the Austrians in the 1890s and later the national library. On the night of 25 August 1992 it was hit with incendiary shells and burned for three days, taking something like two million books with it; people formed a chain under fire to carry out what they could. It reopened in 2014, and the atrium under the stained glass is worth the ticket on its own.

Take the morning train. It leaves Sarajevo, climbs out of the valley and then spends two hours dropping down the Neretva: a reservoir the colour of emulsion, cliffs, tunnels, gorges, and a river that changes from grey-green to turquoise as it warms. It is one of the great short railway journeys in Europe and it costs almost nothing.

Mostar's station is a ten minute walk from the old quarter, or five minutes in a taxi. Drop the bag and go straight to the bridge, and then, if the day is hot, do nothing at all until five.

The Old Bridge was built in 1566 by an apprentice of the great Ottoman architect Sinan, and it stood for 427 years: a single stone arch, 4 metres wide, 24 metres above the water, so steep that it has ribs cut into the paving for grip. It was shelled deliberately in November 1993 and collapsed into the river. It was rebuilt from the same stone quarried in the same place, with pieces dredged out of the water, and reopened in 2004.

Cross it slowly. Then climb the minaret of the small mosque of 1618 on the eastern bank, which has the view every photograph of Mostar is taken from: the bridge, the two towers guarding it, and the green water underneath.

In the evening the divers appear. Men have been jumping from the parapet here since the seventeenth century, a club regulates it, and one of them will collect money from the crowd until there is enough to justify the drop. It takes a while. It is worth waiting for.

Start at the largest mosque in Herzegovina, built in 1557 by the brother of the man who paid for the bridge. It is calm, well proportioned, and much less visited than the small one by the river; the courtyard has a fountain and a graveyard and the interior keeps its painted decoration.

Then the museum of Herzegovina, which occupies the house of the family that produced the region's most famous partisan commander and covers the town from antiquity to the 1990s. It is small, dusty, honest and includes a short film of the bridge falling that most people watch in silence.

In the afternoon, walk west. The boulevard that runs north to south through the middle of Mostar was the front line between 1992 and 1994, when the Bosniak and Croat forces who had been allies turned on each other, and the buildings along it are still shot through, roofless and covered in graffiti; the tall ruined bank at the northern end, from which snipers worked, is now climbed illegally by teenagers. There are no signs and no ticket. It takes an hour and it is the part of Mostar that the day trippers never see.

Come back over the bridge at sunset, when the swifts are out and the stone goes gold.

Two short things before you go, both a couple of minutes from the bridge.

The museum in the tower at the eastern end covers the building, the destruction and the reconstruction of the bridge, with archaeology in the basement and a climb up the tower at the end. It is the best explanation of why this arch matters to people who have never been here.

Then a merchant's mansion of the 1700s on the slope above, kept as it was furnished, with a walled courtyard, a raised wooden divan room and windows shuttered against the Herzegovinian heat. It is also a working hotel, which is the reason it is still in one piece.

Coffee on the east bank afterwards. From Mostar the bus to Dubrovnik and Split takes about three hours, the train back to Sarajevo two, and either way you leave a town that most people saw for ninety minutes and you did not.