There's lots of hotels near heathrow (probably the most i've ever seen!) but on my recent trip we stayed at the Crowne Plaza which was pretty nice. Decent sized rooms and free upgrade to top floor as a Priority Club Plat. We flew in from the US late at night then left again the next morning to Ireland. All the hotels use the "Hotel Hoppa" shuttle buses, which cost about 6 GBP I think. They take you from the terminal right to the hotel.
It probably depends on if you're in any frequent-guest programs - let us know if you have any preferences and then maybe others can comment on other hotels in the area.
Who are you flying with and where from. I am flying out with BA to Boston and the airline got my wife and I B and B in the Hilton - which is connected to Terminal 4 - for £99. Tripadvisor is very good - I checked it out and top of the list was Marriott London Heathrow. But be careful, there are two Marriotts - and confusingly they look the same. I think the other one is Marriott Heathrow Airport or something. I opted for the Hilton because it was half the price. But all Heathrow airports charge an arm and a elg. So shop around on the internet - and if you are unsure which one to book, check them out on tripadvisor. They will also do a pricecheck. But my advice is try other websites - the Far East websites can sometimes come up with good deals.
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My preference is generally the Heathrow Hilton, especially if using Terminal 4 for arrival and/or departure. Its a short walk from T4 to the Hilton, and T4 is a free Heathrow Express ride from terminals 1, 2 and 3.
I generally prefer to walk as its a known and predictable time as well as good exercise after/before a long flight. The BAA Hotel Hoppa buses that serve the local hotels can get full at peak times (like 6:30 - 8am) and you may have to wait for the next one.
If using Terminal 1 for arrival/departure, another option is to take the Heathrow Express to the Paddington Hilton. I did this last time through London. But be aware that the "15 mins every 15 mins" is not always the case. For my return to Heathrow I was on the platform at 5:30am and didn't leave until after 6am due to a faulty train that was eventually cancelled.