This area is fine. There are really no tourists milling around which is nice. It's an average Spanish neighborhood. On the down-side, reaching Plaza Mayor and Puerta del Sol is all (gently) uphill and about a 30 minute walk (maybe 25 minutes if you are in very good shape).
Be sure to take a look at your exact address via
http://www.google.com/maps and take a stroll using the "Street View" function.
Saludos, MadridMan
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