You can try doing a expedia hotel search around Madrid airport for a comprehensive list of hotels.

The closest is the Tryp Aeropuerto which is about 5 mins drive away. There is a courtesy bus. Dont use a taxi who will charge you about EUR 15 for the fare which is the full fare into town.

Nothing fancy but it is decent and clean for an overnight stop. I normally check in at 11 pm and out again at 6:30 am when connecting in Madrid so I cannot comment much.

There is a nicer Sofitel near the convention area. You can take a taxi there and use their courtesy bus to get you back to the airport the next day. You can phone for the courtesy bus from the airport as well if you wish. It has a shared pool with the hotel next door - another Accor hotel but cannot remember which one.