Hotels Near or at Heathrow London GB (LHR)

Nate, we stayed at the Novotel, which was OK. Just OK. But I wanted to point out that there are not a lot (if any) restaurant options around the hotel cluster area, so you'll need to taxi somewhere or eat at the hotel. I'd still stay at the airport, however.

Which terminal will you be flying out from? I usually stay at the PI at T4, which is connected to the terminal by a covered walkway. But, for instance, T5 can be a pain to get to from T4 and if I was flying from there I may choose a different hotel.

We always stay at the Sofitel LHR attached to Terminal 5. They have a wonderful restaurant there,La Belle Epoque, modern French, really excellent, plus they have more casual options, Vivre, bar etc..
You can transfer to other terminals via the Heathrow Express train, free within airport. Or the hotel can get you a taxi if your flight is very early when there are fewer trains. We used a taxi one time to transfer terminals at 4:30 am.
We used to stay at the Hilton which is fine but much prefer the Sofitel. You do not feel like you're in an airport hotel.

We stayed at the Premier Inn at Terminal 4 a couple of times in June. Nice place, cheap rates, and easy access to the other terminals via the Heathrow Express underground train (free) or mini cab which costs about 20 pounds.
They have a full service restaurant and bar, as well as a seperate little cafe/deli for snacks and breakfast items. It's also a short walk via a covered walkway to the Hilton which is located next door.

There are several hotels actually in the airport but there are many many more very nearby, near each of the terminals as well as the old standbys on the Bath Road.

What time is your flight? Which hotel chains do you have points on?

I, too, like the Premier Inn. It is only a few years old, I believe, and amazingly inexpensive. It's clean, decently decorated and not unduly cramped by European-hotel standards. PI rooms are better than one would expect for the price; the chain appears to save money on the service side of things. I'm sure the Sofitel is fancier, and you said "nice", so unless you want to save money (the PI can cost under 50 pounds if you book in advance), you may be happier with a hotel in the Sofitel's class.