Hitchhiking out
South towards Belgrade
To hitchhike towards Belgrade, the best option is to go to Beogradska street (Belgrade's street). There is a nice hitchhiking place just after the city's bus station, but before the road bridge. Its not unusual to see locals hitchhiking here (Google: 45.372437, 20.415726)
West towards Novi Sad
The best place to hitchhike towards Novi Sad is just after the roundabout on the street Novosadski put (Google: 45.379629, 20.350842). You can find this place just by walking in the direction Novi Sad from city center. After around 25 minutes, you will see big shopping mall on your left side and the gas station on your right. Just after few meters from there you'll see the roundabout from where you can get a ride to Novi Sad.