As Alinlondon points out, the Hilton Paddington is at the terminus of the Heathrow Express, but if you're heading out to LHR early, say by 7:00 am, you could probably stay in any of a number of Hiltons and easily make it to Paddington Station in 10 or so minutes. My favorites are probably the Park Lane Hilton (great views from the higher floors) and the Green Park Hilton, in the heart of Mayfair and easy walking distance to Piccadilly Circus and the West End. I've found that the Green Park Hilton often has lower rates and HH Rewards availability when the Park Lane does not.