South towards Belgrade
To hitchhike towards Belgrade, the best option is to go to Beogradska ulica (Belgrade street) located in the southeast of the city, road number 13. There is a nice hitchhiking place just after the central bus station on the right side of the road, just before the bridge. It's 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 east in the direction of Novi Sad from the city center, following the main boulevard (Bulevar Veljka Vlahovića). After around 25 minutes, you will see a big shopping mall (Aviv Park) on your left and a Lukoil gas station on your right. Just after a few tens of meters from there, you'll see the roundabout right after which there is a widening on the road, from where you can safely get a ride to Novi Sad.