Thanks to everyone who answered my Sunday question, I now know that a lot of museums are shut on a Monday. We only have Sat night to Tues morning early so want to see what we can on these days.
Any hints on what to do on a Monday?

Hi Amanda,

The Museo Nacional Reina Sofia, where Picasso's famous "Guernica" is, is open on Mondays. The Royal Palace is also open .

Thank you cruisluv, just wondering if there are any other places or any cafes or restaurants anyone would recommend as well.

I don't think restaurants are related to the museums being closed on Monday.

I think I went to the Reina Sofia and the palace on Monday, as suggested. I think I also reserved that day for major shopping around the Plaza Mayor (souvenirs, etc.) as those shops are always open. You are going to want to see Plaza Mayor anyway.

However, I've read that many restaurants are closed on Mondays in Spain, although I suspect that may be less true in the most heavily tourested areas.

Everything is open on Mondays in Madrid (unless the Prado and the Thyssen Museum, The Reina Rofia is open on Mondays, and close on Tuesdays)
It's not true that the restaurants close on Mondays in Madrid, maybe there is a restaurant closed on Monday, but it's not usual.
I recommend you to go to the "Plaza de Santa Ana", it's a square in the city centre with many bars to drink a beer (caña in Spanish) and eat "tapas". Near "Plaza de Santa Ana", there are many streets with many places to go, like "Huertas" street, with many pubs and restaurants.
Also you can go to "Chueca", Chueca is the gay district in Madrid, but this is not the important thing. In "Chueca" there are many restaurants, shops and pubs, opened everydays. The "Chueca" district is near "Gran Vía" street (underground Chueca).