Hey, I did some research with my parents a year or so back to see schools for me.
The best one to me is the International School in Belgrade. They offer all the stages of the IB program (Primary, Middle Years and IB Diploma). While it is the best, it is also crazy expensive. Tuition is from 8000-23000 euros (and that's not including the capital fee and other fees!). They also don't offer financial aid unless you've been at the school for a long time and have siblings which are also enrolled.
There is also a couple of other schools that offer the English Educational System (i'm not 100% what it's called). The ones that my mom looked at for me were the British Int'l School (they don't offer fees on their website), Prima Int'l School (again no prices), Chartwell International School (it's kind of annoying isn't when the prices aren't displayed). Although the fees aren't listed, the one thing that stood out for my mom is how disproportionate the fees are (based on the standard of living, even for the expat community). Out of the three, my top favorite is probably Chartwell. My sister spent 10 days in their summer camp and she seemed pretty happy at the end of the program.
Now, if you were asking me, I'd recommend the French School (Ecole Francaise de Belgrade). The school doesn't have a good reputation in higher grades, however I do have a good friend who goes there and she is pretty happy. It's also widely recommended by teachers from other French schools abroad. The prices are from 4009 to 4900 eurs (k-12). The students in that school will definitely be fluent in at least two languages (english and french) by the time they finish their education. And French Diploma is a respectable diploma.
So, if you can afford ISB, send your kids there. If not, my recommendation is French, followed by Chartwell.
Good luck
Websites:
-- ISB
-- British Int'l School
-- Prima Int'l School
-- Chartwell
-- French