You'll love Barcelona. Sooo much to see... Casa Mila is awesome. Climb the towers of La Sagrada Familia.. make sure you've had a good night sleep before that hike!!
Some other places to visit... make sure you go to Madrid and Segovia. Madrid will require at least 2 days.. should stay a week!, and Segovia (go to the castle!!!) would take about a day as well. They modeled the castle in Snow White (if I remember correctly!) after the one in Segovia.. it's beautiful. If you have time, try to make it to Andalucia (Granada and Sevilla). I lived in Granada for a year, so I'm definitely biased. There's the Alhambra, Albaicin, teterias (tea shops... so nice and relaxing), the mirador de San Nicholas (an amazing view of the Alhambra and Granada from this overlook!!!), TAPAS!!, night clubs... oh you'd love it! Sevilla is nice as well, but quite large. I have several friends who've lived there, and they loved it. Just make sure you go to Granada!
ALSO.. make sure that the taxi drivers turn on the meter!!!! I've had friends pay 100 Euros for a trip from the bus station to the airport (should only be about 20). This happened in Madrid, but it's known to happen everywhere in Spain!! I'm very serious about this! I had one try to pull that trick on me, obviously unaware that I had lived in the country for a year and was not stupid!
Have a great trip!