i've been to Belgrade for three weeks this summer and I loved it! I recommend checking out Ada Lake (if the weather is good), having a walk around old town and Drocol. there are some cool clubs on barges at the Danube river to check out late at night. Gardoš is fantastic as well - a tower with a view of the entire city.
keep in mind they have no uber, if you need a car you either use CarGo (closest thing I found to Uber) or get a taxi (you can use Viber to order it) - locals recommended Pink Taxi as the best one.