Prado, Reina Sofia, Thyssen (hope you like art).
Wander round the center and sit on a terrace having a beer watching the world go by. Don’t order food in the Plaza Mayor, or indeed anywhere with photos on the menu.
Go for pintxos / tapas in Mercado de San Miguel then walk 500m to the Cava Baja street and have some more.
Retiro park on a Sunday morning.
Wander round Chueca (the gay / alternative area) and go for a meal in one of the restaurants round there.
Clothes shopping in Zara, it’s a lot cheaper in Spain.
Take a train out to Segovia for the day and admire a) the excellent trains and b) the amazing Roman Aqueduct.
If it’s this week there are probably some religious processions. When are you coming?