Good suggestion by liz49. Please post the names of those places/streets you're considering and we'll do our best to help.
Huertas neighborhood is generally a pretty good/cool area. It's my favorite area for hostels (called "hotales" in Spain/Spanish).
There's a youth-hostel (called "albergue juvenil" in Spain/Spanish) in the Casa de Campo (park) but I understand THIS one is in a shady area - and I don't mean "shade" as "under the trees" either.
Saludos, MadridMan
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