Which terminal will you be departing from? There's a Sofitel attached to Terminal 5 and a Hilton att

Which terminal will you be departing from? There's a Sofitel attached to Terminal 5 and a Hilton attached to Terminal 4. And there's a shuttle to other hotels in the vicinity. If your flight's really early, check if the shuttle will be running.
it mostly depends on your budget. The hotels on site are expensive but convenient (though not convenient to every terminal -- that makes a difference too). Some off airport hotels are actually more convenient depending on the terminal.
We stayed at a hotel nearby - The Swan in Staines. It was on the banks of the Thames and lovely - hard to beleive we were minutes away from LHR. We arranged for a taxi and I don't remember the exact price (I'm cheap) and it wasn't maui accommodation guide bad. But we really enjoyed our last night in England there at the inn, much nicer than a souless airport hotel and we had a nice dinner in the pub watching the swans and sculls on the Thames glide by.
We love the Yotel in Terminal 4. Yes, it's a pod, but by the end of our vacation, we're focused on going home. No worries about taxis, strikes, etc. Just get up, take the elevator, and you're at the airline check-in desk.