Finding a quiet hotel in Madrid

In general:

• Try to go to hotels where the whole building is occuppied by the hotel
• Try to avoid big streets or roads nearby
• Obviously, do not choose hotels near night life areas
• Trust in hotels chains like Hilton, Western, etc.. they usually have stronger criterias when they build a hotel
• New hotels better than ancient buildings
• Hotels with fitted carpet are better when other guest arrive very late
• Ask for a room in the highest floors

In Madrid in particular, I can recommend the hotel Husa Serrano Royal. I stay 2 years ago and I don't have any complaint about it, but the truth is that I can sleep anywhere :)

My advice is: find hotels outside inner Madrid (that is roughly the area within the M-30 motorway; a ring road).

Las Tablas, for example, is a new neighbourhood in the north, planned during the housing bubble, and with low occupancy. That means fairly quiet nights (and days). There seem to be an NH and a Holiday Inn nearby. NB: I cannot recommend these two in particular (I haven't stayed); I just suspect they'll be quiet.

Around Suanzes (homonymous underground station; line 5, colour green) there is an Ibis/Accor that can't be expensive. I know those streets, and it can't be noisy at night...

I have been working in Madrid for a while on business and I have sleep problems and I highly recommend the Catalonia Atocha hotel, it has very good prices and is a very quiet hotel and very close to the most emblematic places in Madrid.

A quick google search reveals a couple of links. The first one, from Go Madrid, has this to say about the Hotel Conde Duque:

The Hotel Conde Duque is really a quiet oasis in the bustling city of Madrid. The hotel is located in the peaceful and landscaped square of Plaza Conde Valle de Suchil close to the city centre, so instantly has a more relaxed and inviting atmosphere than many of the other available vacation spots in the city. It is ideally situated near the metro so traveling to Madrid's "must see" attractions poses no problem at all and can easily be done. The rooms here are very clean, with well-appointed bathrooms, many of which have luxurious marble baths. Breakfast is served promptly and is substantial, typical of a four star venue. The setting of the hotel is quaint, overlooking a local playground and park, which is filled every afternoon with children and their families, giving the Conde Duque a real traditional, family feel.

Which may fit your needs. of course, you'd still need to check online reviews for this site, but it's a start - if a hotel is specifically listed on a separate list of allegedly quiet hotels.