1) It would serve as a deterrent against war in the Balkans.
2) It would put us far closer to our potential areas of future conflicts, in the Middle East.
3) Rather than reward the Germans with the income that they get from having American soldiers spending money on their economy, we would allow that money to be spent on the Bosnian/Hungarian economy. That would help to revitalize the region.
The only potential downsides that I see are:
1) The abundance of undocumented minefields and other explosive ordnance that would preclude the use of much land for training areas in Bosnia, until the tedious process of clearing the land is complete.
2) We would need to replace and upgrade the existing transportation infrastructure in Bosnia, to allow for rapid deployment of any heavy forces stationed there.
3) The people in the region may misinterpret this. And, the Arabs might also misinterpret our current presence in the middle east as a precursor to us establishing permanent bases there, as well.