Madrid is a delightful city. I second the Prado, and the royal palace. I not only sesond the Toledo suggestion, but propose the Escorial palace which is a day trip. It is magnificent. Don't bother with the Valley of the Fallen unless Franco's tomb is of interest to you.

I notice that the hotels shown above are quite expensive. Somewhat more modest is the LLIABANY. Near the Puerto del Sol, it is very central and reasonably priced. Enjoy yourself whatever you do!