CCCatharine, I'm sorry to report that there are few (if any) quiet neighborhoods in downtown Madrid. Also, most of the buildings which are now hotels were built in the late 1800s or early 1900s and so few people even had cars so they won't have car parks. Most hotels will direct patrons to the nearest underground car park, mostly likely within a couple of blocks.

It's possible that some of the higher-end 4-star, 5-star, or 5-star GL (grand luxury) hotels have their own in-building car parks but I don't know which ones they might be. Try a few of those listed in the Madrid Hotels page .

Good luck! Saludos, MadridMan