Just to keep the info here accurate. Sorry about the booking BUT I would like to offer my insight of Embajadores.
This neighborhood is just south of Lavapies with easy access to the center. Not even a mile away.
My family lives in the neighborhood and my husband grew up there. It has many parks, is very close to Atocha and if you walk home from the center, it's all down hill. The buses will get you anywhere quickly and the metro too.
The ambiente of the the 'hood is great! Many Spaniards with an increasing diversity from other countries. This is truly a Madrileno neighborhood and very close (walkable) to the city center.