The Gallery of Matica Srpska holds the most important collection of Serbian art outside Belgrade — 18th- to 20th-century paintings and sculpture, displayed in a well-renovated 19th-century building on the edge of the old centre. Free admission and a quiet, contemplative atmosphere.
The strongest rooms are the 19th-century portraitists and the interwar modernists, with a particular concentration on artists associated with Vojvodina. Right next door is the smaller Pavle Beljanski Memorial Collection, which is also worth a look if you have time.