There are a couple of hotels in Hounslow which is the nearest town to Heathrow, the Continental and the Rosemount. Both would be suitable for 1 nights stay and within easy access of LHR. I believe the Continental can arrange transfers, it also has a reasonable restaurant.

In September, an Etap will be opening in Hounslow and the rooms are advertised at £32.

Staines is another option with a Travelodge and restaurants by the riverside. Windsor is mentioned alot but if sightseeing is not required I think Staines would be better since it is slightly nearer.