My place is in the Center of the city, steps from "Puerta del Sol".
Great place because of the location, the people, the ambiance, the neighborhood, pretty close to everything.
Also you have availability to excellent public transports options like Metro or buses.
I guess you will not need them, because of the central location it is possible to walk around to the main attractions of the city.
Puerta del Sol - Av. Gran Via, are the most popular places in the city, you will find great shopping options, cultural activities, Restaurants, Coffee stores.