My name is Jessica and I work with inBed.me (http://inbed.me), a social hostel/bed booking site that allows travelers to see who will be at their hostels before they book and connect with them to share tips and plan trips. Here are some of our best centrally-located accommodations with private rooms:
Hostal Playa: satellite tv/free wifi/you control AC/heat: http://book.inbed.me/madrid/178002/
Hostal Hispano-Argentino- modern accommodations in a historical building: http://book.inbed.me/madrid/161907/
Hostal Loyola- Lots of amenities and the staff are great: http://book.inbed.me/city-center/184329/
Please let know if you have any further questions or if you'd like more recommendations.
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