I took the Metro (subway) to the Estacion de Atocha, and just outside of the station was a place called "Churreria" where we had some Churros with hot chocolate . . . do not miss that, it is fantastic! We walked a couple of blocks to the El Prado museum. We stood in line for about 40 minutes, but it was worth it. El Prado is open from Tuesday through Sunday from 9am to 7:00pm, but they only let people in until 5:45pm. The tickets cost just 3 euros (about US.26) per person. We had a great time there--we spent about 3 hours.
We then walked on the famous Alcala Street to the Plaza Mayor where we enjoyed a taste of delicious typical Spanish dishes: paella, tortilla espanola, and jamon serrano . . . Unforgettable!
Quick Tips:
We also visited Palacio Real and the beautiful Gardens of Sabatini.
Best Way To Get Around:
All the important and juristic places are within walking distance. You can also get a bus that will take you on a tour of the main locations . . . but we had a great time walking.