Crowne Plaza has the shuttle, but is inconvenient (to say the least) for going into Madrid. (and there is nothing nearby).

The Holiday Inn Bernabeu is a good choice, with the metro line to the airport.

Another option is the Holiday Inn Alcala. Although not as central as the Bernabeu, they do offer a low-key shuttle service to the airport. I've only used it from the hotel to the airport though so I couldn't say whether they will also do airport pickups. The advantage is that this property is near a metro line. (very inconvenient to/from the airport, but great for going in and out of the centre)

Piramides is also on the commuter train line that runs to the airport, although this is the furthest away and least convenient for a one-night overnight stay.