Barcelona is capital of Catalonia and world-famous for soccer and architecture. You must visit the cathedral Sagrada Familia, designed by Gaudi, that has been under construction since 1883. Camp Nou, where FC Barcelona resides, is an experience of a different kind.
San Sebastian is a superb beach location just west of the Pyrenees with excellent food (tapas). It should be on everyone's itinerary.
The Canary Islands are politically part of Spain, but closer to Morocco. The islands are mainly volcanic with a very pleasant spring-like climate year-round.
Madrid, capital of Spain and home of the royal family. The city center with great architecture is amazingly small, with nice places to enjoy local food and wines and very walkable.
Pamplona is best-known for its annual "running with the bulls"... Yes, these are real bulls and it is dangerous! Only the very sporty ones that have something to prove, should try this...
Cadiz is one of the oldest cities in Europe. It's location is quite unique, since it is surrounded almost completely by water (similar to Venice). James Bond used the city to resemble Cuba.
Granada is a major tourist destination in Andalusia because of the Alhambra. The nearby Sierra Nevada mountains (3000+m altitude) allow for skiing in winter, with a unique view of the Mediterranean.
Málaga is an important tourist destination, known as "the capital of the Costa del Sol". An estimated 6 million tourists visit the city each year, who usually visit the birthplace of Pablo Picasso.