Barcelona is definitely a city where you can spend lots of time and still not see it all. I have been to Barcelona several times as part of
DCL cruises and still have things I haven't had a chance to see. The
ABD will take you to the big sites, but you may also want to visit other things. I would suggest Montserrat(great museum and you can see the Black Madonna if Mass isn't going on), Montjuic Castle, Olympic Stadium, Picasso Museum, Casa Mila, Casa Battlo, Dali Museum(Figueres, Spain). Barcelona is very easy to get around and they have a very good and easy to navigate metro(subway) system. Besides walking, the metro and the city buses were my primary mode of transportation while I was there. If you decide to take a taxi, not all taxi drivers speak English. Having the address and name of where you're going written down helps.
Montjuic is a huge facility and has lots of other things besides the castle, fountain, etc. They have a bus that goes around the area, so you don't have to walk it all if you don't want to. The only other word of advice I would give you is that, according to the guidebooks, pickpockets are very active in Barcelona. While I was never affected, I heard stories from other DCL travelers who were victims. This information isn't to scare you, just make sure you don't have anything in your pockets that you don't mind losing and that you keep a close eye on your belongings. Enjoy Spain. I'd love to hear how you like the trip. It's on my list, just a little farther down.