Try the Room Mate Alicia Hotel on Prado 2, Madrid City Center. It is located on the Plaza de Santa Ana in a lovely atmospheric neighborhood (old architecture, antique stores, theaters and many restaurants). The plaza itself has several restaurants with outdoor seating where you can eat tapas or dinner and watch locals and tourists late into the night. It is a short 5-7 minute walk to Puerta del Sol (metro and city center). I have stayed there twice. Price is around $80 -$90 for a double (I checked current rates). Not luxurious but has all amenities and service is excellent. Contemporary decor. Check out the reviews on TripAdvisor.com. I stayed there on my last trip because I like the neighborhood and the convenience of being able to walk everywhere (near most tourist sites: down the street from three museums, near Plaza Mayor, Mercado San Miguel). Any hotel near this Plaza would be a good location. I also stayed at the Hotel Quatro Puerta del Sol, Sevilla 4 ( around $90). It is on a busy street just north of the Plaza Santa Ana and across from a bus stop - nice room and good service. I would not recommend staying on Gran Via (too commercial, chain stores) or Puerta del Sol (generally more expensive and noisy). Booking.com has a map feature where you can see where the hotels are located. If you want something a little more upscale let me know.
You asked if I would send my mother there...yes because I am the mother
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