Correct.

Re accommodations in/near Hampton Court -- the apartments inside the grounds book up months - sometimes a year - in advance. There is a lovely hotel just across from the castle. Can be a bit pricey depending on the date but very nice - The Mitre. Also the King's Arms is very close.

Teddington/Kingston-upon-Thames/Hampton Court/anywhere in that general area would be more complicated re transport from LHR but for a 2 night stay it would be lovely.

Transport form Teddington to Hampton Court couldn't be easier. Just hop on the bus. You tap you credit card, and it whisks you there. Easy as pie. I loved the Park Hotel, very nice in every way and really good food. Highly recommend the breakfast, and I also had lunch there which was quite delicious.You can order breakfast from a menu or you can partake of a fairly elaborate continental breakfast spread. We ordered from the menu and were very pleased. It's a great village to walk around. You can get from Heathrow to Teddington by public transport, but we arrived vary late at night and decided to take a cab, which is admittedly expensive. But fast.

When we got to Heathrow to return to the US, it was not the day of the big computer meltdown, but it was the next day. Chaos reigned supreme. We barely made our flight. We followed orders on which line to stand on, but I think by that time the BA guy was just pissed at everyone. After two hours of not budging, we broke off and found a line that got us through pretty quickly. It was all done with automation, no person checks you in, but the machines were malfunctioning. Finally got one to work. Do whatever you can do give them your passport and all other info in advance of going to the airport. I am feeling that 3 hours is a good rule of thumb.

Did you say when you are traveling?

"Transport form Teddington to Hampton Court couldn't be easier"

I meant transport to/from LHR. Heck, I've walked Teddington to Hampton Court Palace.

Oh yes, it would be a nice (long) walk or a bike ride, both through Bushy Park. Where you will see deer mulling about, large ones with big antlers.

From LHR, you takes the Picadilly lIne one stop, and then there is a bus that goes to Teddington.

Before going to Hampton Court, I thought it was loads of fun seeing this Tiny Desk Concert:

I have decided to just stick with the Windsor idea. I am fine with going to Windsor via public transportation from Heathrow. But, to get to the airport for my flight to the US, I will be taking a cab. I never want to risk missing my flight back to the US.

I still haven't booked a place (and many have no option but non-refundable), but I am thinking I may book at the Sir Christopher Wren Hotel in Windsor. It seems to have a convenient and lovely location right on the river.

Have a look at the George Inn in Eton too.

https://www.georgeinn-eton.co.uk/accommodation/