My first piece of advice: drop the American Studies idea. Birmingham has one of the top English schools in England, however the inclusion of American Studies in your degree will do nothing to further your prospects and will give your degree that 'mickey mouse' taint.
Birmingham Uni is indeed a campus uni, and is about a half a mile from Broad St (undoubtedly one of the best places in the UK for going out) and just a little further to the shopping centre, which includes the Bullring.
The campus itself is extremely spacious with a lot of great architecture. The best place to live is definitely on the Vale, which is like a large spacious park with a lake and accomodation around the edge of it. This is also only a very short walk from campus. Very easy to forget that you're within walking distance of the centre of Birmingham!
Regarding the city's reputation. Things have improved a lot in the last 10 years. Brindley Place and the nearby canal provide a really classy environment. Broad St has a load of clubs and you can guarantee there is something big going on every night. The Bullring is one of the largest indoor shopping centres in the country, and this is along with heaps of other shops. Next to campus is Selly Oak where you are guaranteed a great student atmosphere, student pubs and places to eat (remember, Brum is balti capital of the world!).
Hope that helps.