Serbia in 2-3 days
Belgrade could easily fill in a long weekend, but if you can fit it in a day trip to Novi Sad would be worthwhile. While in Belgrade, don’t miss the Kalemegan Citadel, which towers over the city, and some of the ‘secret’ bars that are a great place for a drink or five.
Serbia in 7-9 days
Spend 2-3 days taking your time exploring Belgrade, then head north to Novi Sad for a day or two, taking in Sremski Karlovci (a charming nearby town) and the monasteries. Further north is Subotica, a relaxed town near the Hungarian border, which would well be worth a day or two.
Serbia in 2 weeks +
You could see quite a bit of Serbia in two or more weeks. After Belgrade, and Novi Sad and Subotica in the north, you could head south to Despotovac for some country towns and the big Manasija Monastery.