Reina Sofia museum is always a good idea. And it's never enough of Picasso's Guernica as well as the other modern art gems. Save some hours for visiting and then look round the corner and have some wine at NuBel.
Secret cocktail bar set in a 17th century library. From the outside, it looks like an old charming bonsai shop. You can only access with reservation. To make the experience even more exclusive, visitors must enter a secret code in a small and discreet door.
A piece of Egypt in the city centre. This temple, a gift from the Egyptian government, was taken stone by stone from the valley flooded when the Aswan Dam was built. It’s a great place for a picnic in the summer. You can enjoy the sunset and the (grey) skyline of Madrid.