Wonderful apartment and wonderful Madrid experience! This apartment is right in the middle of Madrid. It's easy walking distance from Atocha Station (though it's a bit of an uphill hike, so if you've got luggage or aren't good with walking you might want to take a cheap cab). Once settled you can walk to the Prado, the Reina Sofia, and plenty of restaurants. Many vegetarian and vegan options in the area if that's something you care about. And there's a lovely indoor marketplace a block away that during the day has lots of meat stands and in the evening is a kind of urban food hall with lots of small places to sit and eat and drink.
There are plenty of cabs on the main road and in Madrid you can call an Uber as well.
The apartment itself is so nice! A stylish two floor unit with nice beds. It's right off the main road, but because the windows look into an interior courtyard rather than the main street you don't hear any noise at night.
(If you or someone you are with can't take any stairs at all, be warned that there are a few stairs to get to the elevator. It's a first floor apartment, but I forgot that in Europe that's what we call the second floor in the US.)