While Madrid was once a city that was under the rule of a totalitarian regime, in modern times, it has grown into its own with art, culture, and high fashion. For the art connoisseur or perhaps someone with just an appreciation, the many museums should be on your list of things to do when you visit this city: Museo del Prado and Museo Thyssen-Bornemisza are definite must sees.
Museo Thyssen-Bornemisza also houses modern art in an old hospital building, giving the art itself a unique home. Palacio Real is a striking example of early 18th century architecture, built over the original location of a Moorish fortress. With nearly 3000 rooms, this structure is mind boggling to behold and to explore.
Parque del Retiro is a nice area to visit when you don't want to do much but walk around and relax. The Plaza Mayor is a big tourist attraction with fun little shops and places to eat. And why not go to the Convent of the Royal Barefoot Nuns just to say that you did? You'll get to go on a tour that lets you in on the secret of their shoeless-ness.
Most flights to Madrid arrive at the Madrid Barajas Airport is the way you'll arrive when you fly directly into Madrid and from there, you can take a number of different routes to the various attractions. The subway system is incredibly cheap with 1 EURO taking you as far as you want to go. The metrobus system is even cheaper, so look into that option too. 10 tickets on the metrobus will cost you less than 7 EURO.
When you're staying in Madrid, you could go to AC Santo Mauro or AC Palacio del Retiro for the ultimate in luxury and style. A number of hostels are also accessible, like the Barbieri International Hostel, Top Hostel, and Mad Hostel. You can also book Madrid Motels or in Barcelona, find Barcelona Hotels.