Not far from Heathrow

I assume you mean as an alternative to London. Windsor is very close to Heathrow.

Oxford is nice, and is well connected to Heathrow by frequent coaches.

I'll second what Mary said.

I'd suggest staying in Windsor.
It's very close to Heathrow.
We took a taxi from our hotel in Windsor to Heathrow on departure day for 20 pounds, a couple of years ago. It would be a little more now.
Staying in Windsor before departure would allow you to visit Windsor Castle and have walks around the town, which is full of good restaurants and historic buildings from many eras.
The Thames River runs through Windsor with boat rides leaving from the riverfront pier.

One possible drawback....a friend stayed in Windsor and was disturbed at night by the noise of flights coming and going from Heathrow over her hotel.
My husband and I have stayed in Windsor many times during trips to England and have never heard the planes at night.
So I cannot predict whether you might be disturbed by noise or not.

Three weeks ago, we spent the last night of our trip in Windsor, specifically the Castle Hotel Windsor. A cab to LHR Terminal 5 cost 35GBP from the hotel. I remember the amount because the driver's machine wouldn't accept our credit card, so we had to scrounge for the cash.

We arrived early enough to spend a few hours at Windsor Castle. It was actually the best "last night of the trip" we've ever had. I don't recall any plane noise, or traffic noise for that matter.

https://castlehotelwindsor.com/

What time is your flight?

Unless it's quite well into the afternoon travelling in from two hours away may not be the most prudent idea.

Canterbury is nice for a couple nights as are York and Cambridge.

I'm the friend I think, lol. I stayed in Windsor for 2 nights in May at the Castle Hotel and wrote down times. From my room I could literally hear planes going over every 60 seconds (yes, I'm nuts and I timed it a few times) from 6A to 10-1030P. My room was in the annex building at the back so perhaps my room was not as soundproofed as others. I also do not live where I hear any jet or street noise so it was quite noticeable to me. Obviously I was not in my room all day but I noticed it as I was out and around in Windsor the afternoon/full day/morning of my stay.

I did think it was a good place to wind down a trip. I visited the castle on my full day and ended it with a lovely Evensong service at St. George's in the castle. That was beautiful.

I also paid 35GBP for a taxi ride although my driver took a CC.

How weird Pam! We were on the 1st floor (American 2nd floor), directly across from the Guildhall, and didn't hear a thing!

On the other hand, we routinely hear jets and trains and highway noise at home. And our dogs contribute a certain amount of ambient noise!

I have a British/American friend who travels back and forth - he likes to stay in Richmond.

do you want to be within 2 hours by car or by train/bus?

In Northamptonshire I am about 1:40 to 2:00 from Heathrow by car, but I wouldn't call it "not far".

Regarding Windsor and noise. While Heathrow does not close at night, there are limited flights during the night. To quote the airports own website:

At Heathrow we do not have any scheduled departures between 22:50 -
06:00 or scheduled arrivals between 22:55 - 04:40. This means that
there are no scheduled flights after 22:55 and before 04:40.

Heathrow also has a voluntary ban in place that prevents flights
scheduled between 04:30 - 06:00 from landing before 04:30.

Over 90% of all the scheduled movements that operate during the night
quota period are early morning arrivals and the majority of these are
scheduled to arrive after 05:00.

https://www.heathrow.com/company/local-community/noise/operations/night-flights

But outside those times, planes will depart and land frequently as some have noticed. Whether and how much you will notice them depends on different factors, like wind direction and how the runways are used at the airport.

I was in a room in a separate building - walked out the door by the reception desk to the small parking area and then entered the other building. 1st floor (UK counting, lol), faced a parking lot and a small alleyway. I think I faced south.

I am awake before 6A so I knew it was 6 when the flights started going overhead. Like on the dot of 6, lol.

I'll add that I always appreciate Air Traffic Controllers but doubly so when listening to the amount of traffic they were having to handle.

Pam, I am so very sorry you had all that noise!!
I cannot figure out how we heard no planes when we were there.
I guess we were so tired, we dropped off to sleep as soon as our heads hit the pillows!

Back to the original question.....I agree with what Badger said.

Oxford could be good. Bus/coach service right to Heathrow.
Lots to do in Oxford.

I have my last 2 nights booked at The Castle Hotel Windsor for my London trip next year - glad to hear others endorse this idea.

On the same broad theme as Richmond I know a forum member who stayed in Egham a fortnight ago. Another interesting place, super easy by bus to Heathrow, as easy as Windsor, even for very early flights. As it was on the stagecoach route to the West country it even played a bit part in the news of victory at Trafalgar

Where will you be coming from?

What time is your flight?

Will you have a car or are you relying on public transportation?