Been thinking of places I'd take you to if I didn't have to work. I think the weather's going to be nice (sunny &amp; cloudy, and temperatures from 1 to 13º C which ain't bad; bring a whoolly jumper!). 
Here are some places you might be interested in, in order of Must's and Could's:
1. http://en.wikipedia.org/wiki/Buen_Retiro_Park
2. http://en.wikipedia.org/wiki/Temple_of_Debod
3. http://en.wikipedia.org/wiki/Gran_Via [the Main Street with all the shops I told you about]
4. http://en.wikipedia.org/wiki/Chueca [Madrid's Gay village, very lively and a stone's throw away from Gran Vía]
5. http://en.wikipedia.org/wiki/Puerta_del_Sol
6. http://es.wikipedia.org/wiki/Fuente_de_Cibeles

I'll be the one who organises the trip to Salamanca :) By the way, American meal for tomorrow evening!