Barcelona is terrific. We took a tour of the city on a motorcycle with sidecar and it was the highlight of the trip (go on the night tour if you do it)-this outfit is terrific if you are interested http://www.ridebrightside.com/
Go to Camp Nou if you can--I didn't check the fixtures for May but I suspect there will be a match or two--well worth it
Restaurants: Very fond of 7 Portes (went twice)
Don't stay at the Rambla (and for that matter don't spend much time there either unless you want to have your pocket picked). We stayed at the W and while we were warned that it was too far off the beaten path it was not and far better than the alternatives
Train from Barcelona to Madrid is easy and fast. Trains in Spain are great