The place of Prado is super cute. Although it is not located in a heart of Madrid, you are still close to everything. If you are looking for an apartment in quiet neighbourhood, this would be a right place for you. We spent 10days with a baby at her place. The apartment is only 2 stops away from Atocha train station, and 3 stops from Puerta del Sol. Thus, you can be within 15min in the city center.
Prado is very kind, a really amazing host, therefore, we fully recommend her place for your next stay.