Off by one week. My partner and I will be there the week after you. I think that someone else has posted recently and knows the city well. Sorry I cannot be more specific, but try searching in this forum.
My own plan is to do a lot of walking. From prior time spent there, I love to walk the avenues and streets. La Rambla is very touristy, but still worth a stroll, especially if you wander through the side street. I find it lovely. Parc Guell provides some good views as does Montjuic. Not sure if you are looking for bars/clubs if there for V-day.