Barcelona Apartments or Residences

Hi

I'm going to be in Barcelona for a month from 12th August onwards doing a language course, but my language school, Don Quijote, has almost run out of accommodation and have a few rooms left in student flats, although these are 30 minutes walk away from the language school (which is somewhere on the Gran Via).

Anyway... I wanted to stay somewhere central (and I'm not sure how big Barcelona is but would 30 minutes walk away still be in the centre?) and just wondering if anyone had any suggestions about where I can find an apartment or a residence, preferably in the centre - and maybe recommend which areas would be good to stay in?

Would really appreciate any help at all!