I studied at Swansea University - American Studies - included a year at an American University - this is a very cost effective way of doing it. It's only a year, but it may be worth a shot if money is an issue, and many Universities across the UK run similar programmes (but check carefully first as they are all different).
I went to the University of Illinois, in Urbana/Champagne - doesnt sound too exciting but it's 2 hours south of Chicago and two hours north of St. Louis and a bit further on is Indianapolis. The locals are friendly and the University is just a massive campus town, 40,000 students and the local town has a population of about 20,000. Loads of bars you can drink in (illegally if you are under 21 which is a major consideration...) Of course New York City has a University, but so does New York State- which is in the capital Albany - not so exciting. Hope this helped. mrwilliams