The Spanish capital is a mixture of modern and historical architecture. The city life is just like any regular metro city but there are so many historical landmarks across the city that you cannot experience everything in one day.
During my road trip across Spain, Madrid was the first i explored. Madrid Airport is on the outskirts, and it takes an hour to reach the city center.
(Tip: When you are travelling across Europe, try to stay near the city center. Most of the monuments and touristy places are situated there. It will save you transportation cost)
The easy way to explore Madrid is on Hop on Hop off bus, which operates from 10am to 6pm.
There are two routes that you can explore. One bus pass through all historical landmarks. The other one takes you to new architectural landmarks.
Here is a list of places that you should visit if you are in Madrid:
Royal Palace
Temple of Debod
Santiago Bernabéu Stadium
El Retiro
The Prado Museum
Puerto Sol
Plaza Mayor
Mercado San Miguel
Gran Via
Plaza de la Cibeles