Belgrade in 2 days: the fortress, Kalemegdan and Zemun

Start the day in Republic Square (Trg Republike), Belgrade's main meeting point and the place where city tours set off. The monument to Prince Mihailo Obrenović in the middle is by the Venetian sculptor Enrico Pazzi and was put up in 1882. On one side stands the National Theatre, modelled on La Scala in Milan; on the other, the National Museum. Founded in 1844, it is the oldest museum in the country and has occupied this 1903 building since 1952. Its most precious item is the Miroslav Gospel, written around 1190 and listed in UNESCO's Memory of the World Register.

Walk from the square into Knez Mihailova. The street runs over the remains of Roman Singidunum, links Terazije with Belgrade Fortress and Kalemegdan Park, and is protected by the state. Along the way you pass the building of the Serbian Academy of Sciences and Arts and the Belgrade City Library, whose basement Roman Hall keeps the remains of a Roman gate and aqueduct. The Tourist Information Centre at number 56 hands out free maps and brochures. Have lunch in the centre and carry on towards the fortress.

Belgrade Fortress stands on the ridge above the meeting of the Sava and the Danube and is divided into the Upper and Lower Town; the whole site is presented as an open-air museum. Climb from Kalemegdan Park to the Upper Town and take in the view of the two rivers beside the Pobednik (Victor) monument. The work of Ivan Meštrović, it was put up in 1928 and first stood in Terazije Square. Among the buildings of the Upper Town are the Tomb of Damat Ali Pasha and the Clock Gate. In season you can enter paid sites such as the Roman Well and the Casemates.

Round off the fortress with the Military Museum. It occupies a building put up in 1924 for the Military Geographical Institute and shows weapons, uniforms, flags and decorations. In the open area around it stand 18th- and 19th-century cannons and heavy artillery from both world wars. On a rainy day it also works as the indoor complement to the fortress.

Head south from the fortress into the cobbled lanes of Kosančićev Venac. This small quarter keeps something of its 19th-century feel; Princess Ljubica's Residence and "?" (Znak pitanja), presented as Belgrade's oldest tavern, are here. Close by stand the Orthodox Cathedral (Saborna crkva) and, opposite, the Patriarchate building that houses the Museum of the Serbian Orthodox Church. The quiet streets above the Sava make a good pause after the busy centre.

Finish the first day in Skadarlija. This cobbled street became the city's bohemian quarter in the early 20th century, when actors, writers and painters settled here; the house of the writer and painter Đura Jakšić became a meeting place for poets. The Tourism Organisation of Belgrade likens the quarter to Montmartre in Paris. Traditional food and urban folk music in the taverns are part of the evening; take the street slowly.

Begin day two at the Saint Sava Temple on the Vračar hill. One of the largest Orthodox churches in the world, it stands, according to tradition, where Saint Sava's remains were burned in the Ottoman period. Saint Sava was the first archbishop and founder of the Serbian Orthodox Church. The church's silhouette can be seen from much of the city, and the square around it is quieter in the morning.

Walk from the church to the Nikola Tesla Museum on Krunska Street. It occupies the family home of the industrialist and politician Đorđe Genčić, built in 1927. Visits are by guided tour, starting on the hour and lasting about 45 minutes, with working models of Tesla's machines, his personal belongings and a film about his life. Tours run in English and Serbian; the afternoon English tours can fill up, so the morning is the better choice.

After lunch, take bus 15 from Zeleni Venac to Zemun. The Tourism Organisation of Belgrade calls Zemun "a city within a city": narrow streets and buildings from the Austro-Hungarian period give it a different feel from the centre. Climb Gardoš hill, where Zemun's landmark, the Millennium Tower, stands within the 14th-century fortress; locally it is known as the Janos Hunyadi Tower. Its balcony looks out over the Danube and the city.

Walk down from Gardoš to the Danube and follow the promenade. The riverside restaurants are known for fish dishes and urban folk music; stuffed zander (smuđ), called the king of the Danube, is one of the best-known fish dishes in Serbian cooking. The walk along the river is the calm part of the day after a busy morning; to get back to the centre, take bus 15 or a taxi.

If you still have energy, spend the evening in Savamala on the promenade along the Sava. The Tourism Organisation of Belgrade describes it as a district where young people go out until late. Walking along the river below the fortress lets you see the first day's views from below.