If you only have one day for central Belgrade, the best way to see it is on foot — the old town is compact and everything essential is within reach.
Skadarlija. A cobbled bohemian street with old-school taverns and live music — best visited in the evening when the taverns fill up and play classic Belgrade songs. By day it's quieter and good for photographing the 19th-century façades.
Kalemegdan Fortress. Roman, Byzantine, Ottoman and Austrian layers of history in one place, with a park stretching to where the Sava meets the Danube. The view from the Victor monument is a must on any first visit.
Knez Mihailova. The main pedestrian street linking Republic Square to Kalemegdan, full of shops, galleries and cafés — a natural route between the other two stops.
Studentski Trg and Dorćol. If you have more time, continue on to Dorćol — a quieter neighbourhood with street murals, smaller restaurants and a different pace than the centre.
For accommodation in this part of the city, browse apartments in Belgrade — most listings are in the centre, a short walk from all of these spots.