Travel
Air Serbia offers direct flights from New York City (JFK) to Belgrade (BEG). Belgrade is an amazing city to visit and spend some time exploring. If possible, rent a car or take a bus to go see Vršac - it is about an hour and a half from Belgrade (very close to the Romanian border as well). Small towns in between, one of them being Vladimirovac which is where the wedding will start.
Novi Sad is another great city to visit, which is North as well but more West towards the Hungarian border. Zlatibor is another well known small tourist city.
Central Serbia is another option, never really been besides driving through, but it is more mountainy. Niš is another big city to visit and explore in that area.
Rental car would be the ideal mode of transportation but you also have many buses and trains that run between all of these major cities.