Money can be wired to a bank in Serbia, no issues with that. However, our financial authorities are pain in the... you know what. You have to explain source of funds for taxation purposes etc.
If you are talking about larger amounts, then it would be one-time (or in 2-3 transactions) stuff, but I would personally prefer an American-issued DEBIT card (better that way), and withdraw when you need it.
If you expect, as you said, many but small transactions, if you can set it up in the US, and just withdraw in Serbia, then you will have no problems. Banks DO charge you a bit, but not close to what they would for wire transfers.