Persal is a hostal, not a hotel. The location isn't bad, home of the restaurant Ginger, on Plaza de Angel, just down from the NH Hotel Tepa and ME, but the experience will not be quite the same. Hopefully you're not there when they have a jazz night.

Room Mate Alicia great location but tiny room-still can't understand the open concept of the bathroom-no door /glass wall!Breakfast used to be free but now they charge but you do get a green apple on the nightstand! Check their wbsite sometimes they offer a better rate than booking.com

We stayed in the Spain Select apartment that maimaitom mentioned (lope de vega I I) and could not have been happier. The apartment is in a fantastic location -walking distance to everything, yet on a quiet residential street. New and modern amenities in the apartment. We were there just about a month ago and would definitely stay there again. I was happy that we didn't choose an apartment on a plaza as it would've been quite loud. Spain Select is a very professional and established company.

Thank you Robert, Chapla, and cmm.

The Persal has become a family joke, as it a place we stay in Madrid whether we like it or not. It is just for one night. The Tepa was almost three times the amount.

We stayed at a quirky bathroom arrangement in Antwerp and once again it is one night. The Room Mate website is about the same price. I also think Room Mate is funny in Spain as mate in various conjunctions of matar means to kill.

We will much more selective as to where we chose for the apartment for a week.

Thank you Kolivier, we look into your suggestion. We are in the US.

We chose a place from Airbnb. There were a few places that we liked in Salamanca and Retiro but did not work out for one reason or another including price and the cancellation restrictions. It was also odd a number were directly on Paseo del Prado, Calle de Atocha, and Calle de Alcala and we did not want to stay on a main thoroughfare.

So we found a place on a quiet street in Chueca, Travesía de San Mateo near the Tribunal and Alonso Martinez Metro stops.

Yes, I know I said I did not want to stay in Chueca but we have never stayed here. We will live.

Thanks again for everyone's suggestions, believe it or not we looked into almost every one of them.

I recently found myself wandering in this area of Madrid and loved it! It is not what I think of as typical Chueca. I'm sure you will enjoy it.

If you go to Sevilla during your September stay, I recommend to attend a concert at the Bienal de Flamenco. I could go to Spain for any of the following concerts alone:

Eva Yerbabuena in the grand Maestranza theater on Sept. 11, Maria Pages in the same theater on the 14th, David Palomar in old world Teatro Lope de vega on the 15th, Estevez and Paños in cutting edge Teatro Central on the 18th, Javier Baron etc in Teatro Lope de Vega on the 20th and, perhaps above all, Dani de Moron, Israel Galvan, Rocio Marquez etc in the Real Alcazar gardens on the 21th. And plain fantastic Olga Pericet in Teatro Central on the 23rd and Pastora Galvan in Teatro Lope de Vega on the 28th. Jam packed with highlights.
http://www.labienal.com/programa/

Some teasers:

Eva Yerbabuena: https://www.youtube.com/watch?v=clCZYH5VNWw
Olga Pericet: https://www.youtube.com/watch?v=632-AtbOjvE
Israel Galvan: https://www.youtube.com/watch?v=BTXf01hRr94
Estevez y Paños: https://www.youtube.com/watch?v=ReA2JKJ2HCs
Pastora Galvan: https://www.youtube.com/watch?v=k2SBUcrJgeQ
David Palomar: https://www.youtube.com/watch?v=CnkubQ-u8Ns
https://www.youtube.com/watch?v=lFWQIliO2Mg

Thank you Kimhe, I always appreciate your expertise and generosity with your knowledge, but we are not planning to visit Sevilla. During the 8 days in Madrid we may take the AVE for a day trip to Ceunca or overnight trip to Valencia.

We will go for a day to Toledo and while in Madrid go to the Prado, Thyssen, and Reina Sofia.

We will also go to our favorite store in Madrid Casa Hernanz and Cortes Ingles for a batido and the Mercado San Miguel.

http://www.yelp.com/biz/casa-hernanz-madrid

Thank you Chapla.