Last time we were in Madrid (just pre-Covid) we found La Platería Bar Restaurante just off the Paseo del Prado on the west side of the paseo, kind of across from the Prado museum, just north of CaixaForum (address: Calle de Moratín, 49 c/v, C. de las Huertas, 82, 28014 Madrid, Spain). This is within decent walking distance of Atocha station. We went there several times for dinner and lunch. Food was excellent, LOTS of locals eating there and they open a little earlier than most places for we Americans who might like to occasionally eat a little earlier than the Spanish norm. The neighborhood around there is lovely, ripe for exploring, and I'm sure there are numerous places to stay. We have always stayed at the Westin Palace Madrid, which is huge, yet does have a smallish, pleasant feel! It is a beautiful hotel worth the splurge if you can, staff is outstanding. Not quite what you mentioned, but just in case...
Enjoy your trip, Madrid is one of our favorite cities, that deserves many days!