First established in Pest (part of modern Budapest) in 1826 and moved to Novi Sad in 1864, this is one of Serbia's most important and long-standing cultural institutions. It's not a mere gallery but rather a national treasure, with three floors covering priceless Serbian artworks from the 18th, 19th and 20th centuries in styles ranging from Byzantine to modernist, with countless icons, portraits, landscapes and graphic art (and more) in between.
It often hosts interesting temporary exhibitions as well; see the website for upcoming events. On Fridays at 6pm, the museum offers expert interpretative tours (in Serbian; 1000RSD) of the permanent collection and/or current exhibition. For English or Italian, arrange one week in advance.