Niko Bellic is Serbian, but a very poorly portrayed one. I'm from Slovenia (ex-Yugoslavia) so I slightly know the language and while I admit it's very poorly spoken it is pointed out many times that he's from the Balkans. Right at the start Roman says that Niko's English is better than his Serbian.
I had some troubles with recognizing the language, because it is usually mispronounced. Some phrases that I managed to catch are (there are more but it would be too long):
"Ti si dobar u ovoj igri?" (Are you good at this game?);
"Uvijek isto nikad drugačije" (Always the same, never changes.);
"Ovdje sam zbog tebe drkadžijo. Otvori!" (I'm here because of you, w*****. Open!)
His first name is more Croatian than Serbian and surname Bellic wouldn't exist in the Balkans, because they don't have double letters (the way characters are pronouncing it in the game makes it sound more like a Russian last name - Bellik, but instead the name should be pronounced like Bellich with ć).
There are many errors, but I still think Niko is meant to be at least from the Balkans, if not exactly Serbia. No way he is Russian.