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.
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...
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.
Ronda, Andalusia, is known for its cliffside location and a deep canyon that divides the town. Both sides are connected by an ancient viaduct. Another point of interest is the, now not used, arena for bull fighting.
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.
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.
Segovia is located just north of Madrid and very well worth a day-trip. The main sights are the old city center with large Roman Aquaduct, the Cathedral and the Phantasy Castle by Alfonso II.