I too would seriously steer clear of Las Ramblas for accommodation - it's a great place to look at the market stalls and street performers, and there are some good cafes to have lunch, but it is also rife with pickpockets and hotel thieves preying on tourists. Don't bother with the cheaper hotels around Las Ramblas as a lot of them double as brothels.
jrtv's given some good websites, so check them out.
Last time I went to Barcelona I stayed in one of the suburbs, Gornal, which was much cheaper and not at all touristy. The brilliant thing about Barcelona is that it has an excellent public transport system. Last time we went, we used the tube trains to get to the city centre. They cost next to nothing and were clean and punctual.
Hope you enjoy your visit. I'm very envious. We've been there about six times and still haven't seen everything.