Madrid and the cities of Toledo and Segovia, all driving distance from Madrid, have so much history and flavor that you will need months only to cover the most important aspects of Spanish culture. I will try to tell you about what is most important and fun. Madrid is the capital which has major museums and shops. A great time will be spent in the Prado museum and walking down La Gran Via, a major shopping street. Toledo has El Valle De Los Caidos, a memorial to the fallen in the Spanish civil war. Segovia has both food and history; they still have a roman aqueduct, which still serves parts of the city.
Quick Tips:
Plan to stay at least a week. Five days in Madrid and one day for every other city I mentioned. Start with the old Madrid, continuing with the new Madrid. Try to visit landmarks in the morning while doing shopping in the afternoon. Remember that stores close for two hours after lunch for a siesta. Best Way To Get Around:
Rent a car to move outside Madrid, but use taxis while inside. The parkings are nonexistent while the driving is wild. I have heard that the public transportation is adequate, but I have never used it.