Talk a walk around El Retiro park and pass by the glass house and the vegetable garden 

Museums that are worth spending a morning or afternoon at: 

Spend the day or two shopping in Salamanca (around cala lagasca, c de claudio coello, c de seranonis behind them but that's more high end known brands) 

Want to change from having a sit down meal? Visit the Mercado San Miguel and try the different types of food from Spanish tapas to seafood delicacies to artisanal desserts 

If you are in Madrid on Sunday, go to the El Rastro flea market and you will find unique souvenirs or even something small for your home that will remind you of your trip 

This probably should go under what to eat, but it's a staple in Madrid that you should plan to go eat churros and chocolate at the famous 18