Four days in Split: a Roman palace people still live in

Walk in through whichever gate you land nearest and aim for the middle. The Peristyle is the colonnaded courtyard at the heart of the palace, where the emperor appeared under an arch to be acclaimed as a living god, and where a black granite sphinx shipped from Egypt still sits at the side. It is now where the town drinks coffee.

The little temple beside it is the best preserved Roman building in the complex and takes ten minutes. Its coffered stone ceiling and the barrel vault above the door are original, which is remarkable given what happened to the rest.

Then eat. The palace is at its best after nine at night, when the coach parties have gone and the stone gives back the day's heat, and the lanes north of the Peristyle are full of tables.

Be at the cathedral when it opens. It was built as Diocletian's mausoleum, an octagon ringed with columns, and turned into a church in the seventh century by the Christians whose religion he had spent his reign trying to stamp out. It is dedicated to Saint Domnius, a bishop executed in that persecution. Whatever else the building is, it is a very long joke at the emperor's expense, and it is one of the oldest structures anywhere still in use as a cathedral.

The bell tower next to it went up in stages from the thirteenth century and was rebuilt around 1900. The stairs are steep, open at the sides and not for anyone who dislikes heights, but the view takes in the palace roofs, the harbour, Marjan and the islands beyond.

In the afternoon go west, up onto the hill. Marjan is a pine covered ridge with paths, chapels and coves, and the road along its lower slope leads to the gallery Ivan Mestrovic built as his own house in the 1930s. Croatia's best known sculptor left it, and the work in it, to the state. The chapel a few hundred metres further on holds his wooden reliefs of the life of Christ and is included on the same ticket.

Trogir is a small island town between the mainland and the island of Ciovo, joined to both by bridges, twenty five minutes west by bus and rather more pleasantly an hour by boat in summer. Bus 37 from Split runs all day and stops at the airport on the way, which makes this a good day to do if you are flying out from there.

The whole old town is on the UNESCO list and it is walkable in an afternoon: a cathedral square, a loggia, a ring of stone lanes and a waterfront promenade. The cathedral's west door is the reason to come. Carved by a local master named Radovan in 1240, it crowds Adam and Eve, the months of the year, hunting scenes and a nativity into a Romanesque doorway, and it is one of the great pieces of medieval sculpture on this coast.

At the far end of the island, a Venetian fortress guards the channel. You can walk the walls and climb the tower, and in summer it is used for concerts.

Eat by the water, take the late bus back, and you are in Split in time for dinner anyway.

The last morning goes north, twenty minutes on foot from the palace, to the museum that holds what was dug out of Salona: sarcophagi, mosaics, glass, and the inscriptions of a Roman provincial capital that had tens of thousands of people in it before Split existed. It opened in 1820 and is the oldest museum in the country. The arcaded courtyard of stone fragments is the best part and much of the labelling is in Croatian only.

Then walk down to Bacvice for a swim before you leave. The bay is five minutes from the ferry, bus and railway terminals, which makes it the easiest goodbye in Croatia: a shallow warm bay, a sandy bottom, and locals playing a ball game in the shallows that they take more seriously than you would expect.