Hotel at Heathrow

try the Premier Inn

https://www.premierinn.com/gb/en/hotels/england/greater-london/london/london-heathrow-airport-bath-road.html

Sheraton Heathrow

There are lots of hotels at Heathrow, some within the terminals or so close as to not make much difference, or dotted around the outer perimeter. My option is to go via booking.com and filter the results using the Terminal you are arriving or departing from. Usually on that site the distance from the terminal is given which allows you to make a judgement.

I'm down there next week - Terminal 3 - and will hope to use the free bus that drops off for hotels not within an actual terminal. I mention this because it might be of interest to you as well in making a decision.

Not sure what would strike you as reasonable but you can also filter by price as well.

Hope you find somewhere that suits your requirements.

Ian

I just booked a single at the T4 Premier Inn for the night of September 9. The rate was an incredible £37.50. That's non-refundable; the refundsble ràte was between £45 and £50. I'm probably going to need something in late August as well, and those rates are currently about £20 higher. I don't know whether the variance is attributable to a difference in demand for August vs. September or it's a matter of how far in advance the room is booked.

I stayed at that PI last fall, and it was fine. You can walk there (through an enclosed walkway) from Termimal 4.

I'll add to the recommendation of the Premier Inn, Terminal 4. I stayed there a few weeks ago after the morning flight from Chicago to London. I really liked it, very inexpensive by London prices. I believe this is a relatively new property. The room was perfectly clean, the bed very comfortable, and there's a decent selection on the TV as well as BBC radio available. The bar has a very international selection of beers available. The breakfast buffet was priced higher than I'm accustomed to at Premier Inn, but I assume that's just London prices. The food was excellent.

That Premier Inn suggested in the 1st post is where my daughter and I stayed 2 nights before traveling back home. They were good, comfy bed, no frills, but quiet and comfy.
The problem we did have was that we booked places on their shuttle to heathrow, and it never showed up. I called a cab and we barely made it to our flight. Could have been an exceedingly rare situation, but I never did get my refund like they said they would do. :( Oh well, got the room at £29 per night. Fair enough I guess.
Have fun!
-Alison

That is why I really like the T4 PI: I can walk to the terminal and use the regular airport transportation, without depending on a hotel shuttle.

In the past month I stayed twice at the new Premier Inn connected by covered walkway to Heathrow Terminal 4. I was very pleased by my room and loved the inexpensive cost (esp. compared to the Hilton, just across the road).

Thank you all so much for the advice. Premier Inn sounds like the place to be.