There are three major art museums: El Prado, Reina Sofia and El Thyssen
if you have to chose just one, I would go to El Prado. For modern art The Reina Sofia. There are always a lot of free art exhibits sponsored by private corporations al around the city. If Im not mistaken theres a Francis Bacon one in El Prado right now that is a must.
You can visit La Puerta del Sol, Plaza Mayor, El Palacio Real (the Royal Palace), the Plaza Cibeles, the fountain of Zeus. Madrid is a great place to immerse yourself in history. Have walks on the Casco Viejo (the older part of the city).
Go to el Retiro, a big park where there are a lot of things to do, especially on weekends (street theatre, mimes, boat rides
) and take a look at the crystal palace there; the botanic garden is also nearby.
The Warner theme park is always a hit with the little ones.
Use the Metro (subway), but try to avoid rush hours (8:00-9:00, 3:00-4:00). You really dont need to rent a car or take lots of taxis if youre staying in the center of the city.
The whole family can go into a bar (family friendly places that are more like a café) and order a few tapas and mosto (grape juice) for the kids.
The Cathedrals of Almudena and Los Gerónimos are beautiful places to visit, their architecture is amazing.
Toledo is really close so is a great a day to visit it for a day. You can go by bus.
The people in Spain are very friendly, youll have a lovely time there.