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.
Seville is the capital of the Andalusian region that also includes Malaga and Granada. It is very Spanish here with historical buildings, Flamenco Music & Dance, horses, Paella and Sangria. Note that it can be really hot (40°C and more) 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.
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.
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.
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.
Jerez is known mainly for two things: 1) the bodegas for the finest Sherries and 2) the Equestrian School for ultimate horse back riding demonstrations. Add to this great weather, some flamenco and lots of orange trees and then you know something about Jerez de la Frontera.
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.