Which terminal do you fly out of? If it's T2 or T3 then you might want to stay at Paddington as the Heathrow Express is as fast as the hotel shuttle (albeit a bit more expensive, but there are some advance purchase deals you would qualify for).

If you're in and out of T4 or T5 (same terminal) then stay at the Hilton or Sofitel respectively and use the underground to get into London.