I've been to Barcelona once and loved it!
Must see is Gaudi's Cathedral (not to be confused with the other cathedral which is more central) and of course a trip to Las Ramblas (central part with all of the street artists etc). The architecture in the streets up to the cathedral is just fantastic.
The cable car from Mountjuic is incredible (if not a little scary!), you end up by the beaches and can then walk into the centre.
I stayed quite centrally, but remember that the tube was really easy and very convenient.
However, I did go to Valencia last year and the tube had changed systems - luckily we found someone who spoke English to help!!!
I do hope that you have a wonderful time - take good walking shoes, because there is just so much to see!!!!