Suggested four day London tourist itinerary

Just as a starting point, Rick has a 7 day suggested itinerary. Add or subtract as you see fit. I'd also suggest getting the RS London guidebook.

https://www.ricksteves.com/europe/england/london-itinerary

To start: Westminster Abbey and the Churchill War Rooms are very close to each other. Order your tickets in advance.
Don’t you have a London guide book? If not, buy one to help you plan your four days.
Your hotel is very centrally located and thus getting around will be easy.
As far as using the Tube( like a subway) , check if you have to walk up and down stairs to use the trains. With your recent surgery, taxis may be a much better idea for you.
Enjoy our favorite city!

Get a map of London (paper or online) and locate each of the sights you want to see, plus your hotel. That will enable you to group them geographically and plan your days efficiently. For example, the Churchill War Rooms, Queen's Gallery Mews, Westminster Abbey, and Buckingham Palace are all close together. So are the Tower and St. Paul's. The British Museum is in a different neighborhood but could take most of a day if you choose.

In London the subway is called the Underground or the Tube. (A subway is a pedestrian tunnel under a busy intersection.) You may also find the buses useful -- slower than the tube but you can see where you're going.

The discussion of London under "Explore Europe" above will help you plan, and you might also find good advice under "Travel Tips" above. A guidebook will also be very helpful -- borrow one from your library if you don't want to invest in one.

I would not waste my time on Changing of the Guard. I have never been to Greenwich, but I can highly recommend taking a boat from Westminster Pier to Kew Gardens. I think the British Museum is a must-see, but it is a lot of walking.

I would have Greenwich as a must do as long as you can spend most of a day there. There is so much to see and you have two interesting ways to get there and back - boat and DLR.

1.) Clarity please as there is no Belgrave Hotel in London. Who made the hotel reservation?

2.) The subway is the London Underground, aka the Tube. This website will help you plan your routes:
https://tfl.gov.uk/

3.) Use Google maps overhead view to see how close locations are to one another.

Groupings:
Westminster Abbey
Parliament Building
Churchill War Rooms
Horse Guards Museum and Parade
St James Park

Trafalgar Square and Covent Garden

Buckingham Palace
Queen Victoria Statue
Wellington Barracks
The Guards Museum
Green Park

St Pauls
Millennium Bridge
Barbican Center

Leadenhall Market

Skygarden
St Marys axe ( aka The Gherkin )

There's a Belgrave Hotel in Pimlico.

We are also staying at The Belgrave in September, so I’m really counting on it being there. :-) I hope you like it and will report back if you’re going before we do. I’m following the suggestions you’re getting. great information!

Well, I think a good first start would be to figure out where your hotel is if you do not know that already! While London is a huge, sprawling city, most first-time visitors tend to stay in the area roughly between Tower Bridge to the east and Hyde Park to the west. Your list is pretty much the standard first-timers to London itinerary and doesn't need that much changing in my opinion. Covent Garden is less something interesting to visit and more of just a shopping area with many of the shops no different than what you might find in any U.S. mall. I recommend going there when you need a break from museums or later in the day after you've done your sightseeing. You may also want to research London's famous department stores like Harrods, Liberty, etc. to see if those would be a more rewarding or interesting shopping experience.

Keep in mind that the British Museum is huge. I'd recommend researching what's there and coming up with a plan of your top 10-20 things that you really want to check out. Alternatively, get a copy of Rick's London guide (either new, or a cheap older version on eBay) as I'm sure he must have a British Museum section in there.

You may want to look into the double-decker tourist buses as an alternative to the Underground and taxis. They are everywhere and will take you to most places you will want to go. The cost of taxis add up and the Underground can be brutal to those with physical challenges (no seats on crowded trains, elevators out of service or non-existent, escalators out of service or non-existent, etc. ).

@Johnew52

Pleased to see there is a Belgrave Hotel in Pimlico. Good reviews too.