The question isn't what should you do in Spain, it's how much time do you have! Here's a quick list of attractions you must check out: tapas at Bar Lobo, Gothic Quarter, Park Güell, La Sagrada Familia, coffee and pastries at Forns del Pi, and catch a traditional flamenco show at Tarantos Club Barcelona. Also, churros and chocolate are a must, as is a trip to Barcelona beach.
Traveller's tip: pickpocketing is a very common crime in Barcelona, so make sure to leave sentimental or costly personal items at home and keep an eye (and hand) on your purse at all times.