Within the Petrovaradin Fortress's walls, this city museum has worthwhile exhibitions on the citadel's history, military equipment and Novi Sad civic life between the 18th and 20th centuries (don't miss the gorgeous blue-hued gramophone). There is some English signage; otherwise, the staff are happy to help with explanations.
The museum can also arrange tours (in English; 3500RSD) of Petrovaradin's 16km of creepy, but cool, unlit underground tunnels, known locally as katakombe (though you can see a portion of it with regular museum admission). While their official use was for military purposes, rumours abound of mysterious treasure troves, tunnel-dwelling reptiles and still-roaming ghosts.