Santiago de Compostela is the capital of Galicia and the end point of the pilgrimage "Camino de Santiago". The apostel James should be buried here. The journey here is different from other journeys since people like to either walk or bike.
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.
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.
Cordoba has a beautiful old city center with a lot of charm. The main attraction however is La Mesquita, a cathedral that started as a mosque. Cordoba is one of the hottest cities in Europa in Summer.
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.
Mallorca (aka Majorca) is a very well visited Spanish vacation island in the Mediterranean. Many Germans, Brits and other Europeans spend their vacation in one of the many resorts on one of the many beaches - or just in a Finca in the main land. Some even spend the whole winter there and enjoy the pleasant climate and atmosphere. Palma de Mallorca has excellent connections by air to many European cities.