In this picture you can see the Neptune Fountain in the "Plaza Canovas", in front of the Museo Thyssen Bornemizsa.
Although there are some tourist buses, I think Madrid is a city you have to visit on foot. If you want to go to one of the attractions far from the city center, you can take the metro. There are 12 lines, and metro stops next to most places. The metro runs till late at night.
♥ Visit Tagulandang Island ♥