Why leave the capital
Belgrade works well as a base: two or three hours of driving gets you to mountains, to a spa town, to the Danube and to wine-growing Vojvodina. Most destinations suit a day trip, and some are better kept for a weekend with an overnight stay. Below are routes by type, with approximate distance and driving time.
Vojvodina: close and flat
Novi Sad is about 90 kilometres from Belgrade; by fast train the journey takes under an hour, which makes it the easiest day trip. Fruska Gora is right there: monasteries, wineries and viewpoints half an hour from the city. Subotica is about 190 kilometres away, a town of Secessionist architecture and a synagogue, with Lake Palic and its swimming season nearby. Sremski Karlovci is a small town 10 kilometres from Novi Sad, known for its wine cellars and old centre.
The Danube and the east
The Djerdap gorge is about 130 kilometres from the capital: the narrowest stretch of the Danube, with cliffs, a viewpoint and the Lepenski Vir archaeological museum. Silver Lake, or Srebrno jezero, is about 100 kilometres away, a quiet spot for swimming, fishing and cycling. Nis is about 240 kilometres along the motorway, the country's third city, with a fortress, Roman ruins and Cegar. It is convenient to stop at Djerdap or at Vrnjacka Banja on the way.
Mountains and spas
Zlatibor is about 230 kilometres, the most popular mountain for year-round holidays: walking and cycling in summer, skiing in winter, with developed infrastructure and plenty of accommodation. Kopaonik is about 290 kilometres, the country's main ski resort, with altitudes up to 2017 metres. Tara is about 200 kilometres, a national park of pine forests and Lake Perucac. Vrnjacka Banja is about 200 kilometres, an old spa with mineral springs. The western areas are better visited with an overnight stay: the drive is three to four hours each way.
How to plan the trip
For a single day, choose what is within two hours' drive: Novi Sad and Fruska Gora, Sremski Karlovci, Silver Lake, Djerdap. Leave the mountains for a weekend: the distance is real and you want more time on site than a day trip allows. On motorways between larger cities there are tolled sections, paid by card or cash, so small change in the glovebox helps. Petrol stations are frequent, but fewer in the mountains, so fill up early.
What to take and what to remember
For the mountains you need shoes with proper soles and a warm layer even in summer: evenings in the hills are cool. At Djerdap and in national parks cash is useful, as card terminals are not everywhere. If you drive in winter, check that winter tyres are fitted: from November to April they are mandatory on the roads, and in the mountains chains may be needed. Public transport to spas and mountains exists, but departures are less frequent than in cities, so weekend tickets are best bought in advance.