The city is a little big to walk everywhere and with the cost of public transportation so cheap, it’s better to use that. It’s also very easy to get to many different domestic and international destinations from Belgrade; bus service gives you more departure options and is definitely the quicker way to go. While there are no public buses going to Timisoara in Romania, a private service offers door-to-door shuttle service for a reasonable 20 euros (also offer from Belgrade to Budapest for 25 euros).
For the more budget conscious, there is currently a special from Belgrade to Budapest for 15 euro by train. You can get the same deal if visiting Novi Sad, just ask for the "Budapest special" otherwise they will charge you the full fare of over 20 euros to go from Novi Sad to Budapest.