Four days in Belgrade: no old town to speak of, and the best night out in Europe

Begin at Republic Square, which is the meeting point of the city: a horseman on a plinth, the national museum on one side and the national theatre on the other, and everybody in Belgrade saying they will see you by the horse.

The national museum's neighbours are worth a slow half hour, and then take the pedestrian street that runs northwest from the square. Knez Mihailova is a nineteenth century shopping street built on the line of a Roman road, lined with plane trees, buskers and cafe tables, and it runs for a kilometre straight into the fortress gates.

On the way, drop into the Orthodox cathedral of 1840, a plain neoclassical box with a very ornate interior, where two of the men who made modern written Serbian are buried in front of the door. It is a five minute stop that explains a surprising amount about the country's nineteenth century.

Then Kalemegdan. It is a fortress and a public park in one, with Roman foundations under Ottoman walls under Austrian gates, and the point of the bluff looks out over the Sava emptying into the Danube with the whole of New Belgrade beyond. Locals come here to walk, play chess, push prams and watch the sun go down; go late in the afternoon and stay for it.

Dinner afterwards in Skadarlija, the cobbled street of nineteenth century taverns just east of the square, where the accordion is not optional.

Three of the biggest things in the city, in one arc south from the centre.

The temple of Saint Sava stands on the hill where, in 1595, an Ottoman commander burned the relics of the saint who founded the Serbian church, apparently to break the population's spirit. Three centuries later they started building the largest Orthodox church in the Balkans on the spot. Work began in 1935, stopped for the war and most of communism, and the interior was only finished in the last few years: forty million pieces of gold mosaic under a dome that was assembled on the ground and jacked up into place in one piece. It is free, it is enormous, and the crypt below it is arguably better than the church above.

Then Tesla. The museum keeps his personal papers, his instruments and, in a gilded sphere on a plinth, his ashes, which came back from New York in 1957. The tours are hands-on: somebody will fire up a Tesla coil and hand you a fluorescent tube that lights in mid-air. It is small, it is busy, and tours run in English at fixed times, so check before you go.

In the afternoon, the Museum of Yugoslavia. Tito is buried here, in a white marble slab in a glasshouse called the House of Flowers, with his own residence next door and a collection of the presents he was given across four decades of non-alignment: swords, ivory, moon rock, a lot of taxidermy. The strangest room holds hundreds of relay batons, carried by young people from all over the country every year to arrive on his official birthday. Whatever you think about Yugoslavia, this explains something no book quite does.

Dinner back in town, late.

Zemun is half an hour from the centre and was a foreign country within living memory of the buildings. Until 1918 the frontier of Austria-Hungary ran along the Sava here, and this was the last Habsburg town before the Ottoman world started on the other bank. It still looks like it: low pastel houses, baroque churches, a fish market and a promenade.

Climb the hill behind it to the tower, put up in 1896 for the thousandth anniversary of the Hungarian conquest and left behind when the border moved. From the top you get the Danube, the confluence, the concrete towers of New Belgrade and the old city's bluff all in one turn.

Come down for lunch on the quay, where the fish restaurants are, then walk or take a bus south along the river to the modern art museum at the point where the two rivers meet. The building is a 1965 arrangement of glass crystals in a park, the collection covers a hundred years of Yugoslav and Serbian art, and it is unhurried and almost empty.

The evening belongs to the water. Barges moored along both rivers turn into bars and clubs from May onwards, playing anything from house to brass bands, and the whole city ends up on them. Ask someone under thirty which one is good this summer, because the answer changes every year.

The old quarter below the fortress is called Dorcol, from the Turkish for crossroads, and it is the one part of town where the Ottoman street plan survives even though almost none of the Ottoman buildings do.

Start with the mosque. Belgrade had well over two hundred of them in the seventeenth century and now has one: a small, plain, working building of around 1575, tucked between apartment blocks in a side street. It was set on fire in 2004 during riots and repaired afterwards. Ask before entering, dress modestly, and be quiet.

Then the national museum on the square, which reopened in 2018 after fifteen years shut and is much better than that history suggests: prehistory in the basement, a Roman and medieval floor, and upstairs a serious European painting collection with a Rubens and several Impressionists that nobody expects to find here. Two hours if you have them, one if you do not.

Coffee on the square afterwards, slowly, because that is the correct way to leave this city.