The most memorable moments about my adventure were the day excursions to differnt cities. If you have the time, schedule non-tour trips (the adventure is finding it yourself). I found Salamanca, Segovia, Toledo, and the small town of Escorial.
Quick Tips:
Madrid is home to hundreds of hotels. Many taxi cab drivers will not even recognize your hotel name unless, you provide them with an address.
The menus of the day (El Menu del Dia) at the restaurants will not only be appetizing to you, but will save you some euros. If restaurants do not post it outside, ask within.
Best Way To Get Around:
The most efficient way of getting around Madrid is by cab. However, if you stay at a hotel that is centrally located, walking is your best bet. I was very impressed by their transit systems (trains and buses). The metro - "the subway" - is also an excellent way to explore the city.