National Park Tara is a nearly 50,000 acre mountainous hiking and camping spot near the Bosnian border. I spent two days staying at Hotel Omorika (about 17 euro for a single room a night and includes breakfast and dinner) at the edge of the park and went on a few lovely hikes. I saw a fire salamander, great views of the gorges in the area, and loads of gorgeous flowers.
An easy half hour bus ride from Novi Sad, Sremski Karlovci is a lovely little town which offers access to national park Fruska Gora. The park is supposedly an expansive hiking spot, but in the boiling August heat physical exertion was a bit out of the question. Instead, a NYC friend and I hired a private taxi driver to take us on a tour of the monasteries in the area. The very helpful tourist office in town helped us to arrange it.