I very much enjoyed my stay at Noe's (1 night before a flight out of town) - the home seems recently renovated with contemporary furnishings. The home was clean and it was easy to reach Noe. Convenient location.
I later stayed a bit further north in Madrid and enjoyed that experience as well. I would be interested in the Salamanca district as it seemed to be primarily locals; I think a central location in Madrid is great for a first time visitor so that you are never too far away from whichever neighborhoods most resonate with what you are looking for.
I would be happy to stay here again!