it should work but would probably need to be a Tri-band as in general I think Europe uses 2 specific bands and the US uses a different third one.
I would find out which band your current network uses before you go and ensure that the phone you are buying supports this band.
If the phone is locked in any way to a US provider, virtually all phones can be unlocked from free to about £15. Again, best to check the model either before you go or on the Internet whilst you are there.
I don't think phones are much cheaper over there so it's best to take with you an unlocked tri-band phone and then buy a pay as you go equivalent simcard on a US network to cut down on your call costs. That's what I will be doing anyway....