First Visit London!

Just 2 notes:
Highclere is not always open, be sure to check your dates.
You can walk the Abbey road area by yourself. There aren't really many Beatles sites in London, and the London Walks Beatles tour we took was our least favorite.

I lived in London for 20+ years, and still visit regularly.
Sheekeys and Rules are both great choices.
If you want another splurge, the newly reopened Simpsons in the Strand is getting good reviews and is now on my list.
Any time I'm away in a city, we always take the HOHO bus for a rest and for orientation.
If you need more WW11 experiences, the Imperial War Museum near Waterloo is a good bet, and possibly a day trip out to Beltchley Park.
The Henrietta looks good, too, but be sure to request a walk in shower if this matters to you - I can no longer safely climb in and out of a bath.

. But then I realized it really serves a purpose--so...maybe we take a London HOHO.

I would suggest you avoid these. They can’t use bus lanes and you will spend a long time sitting in traffic listening to out of synch recorded commentary which is mostly incorrect. If you want to go on a bus you can, you know, get on an ordinary bus.

You are not going to be able to walk to all attractions. For context London covers more than 600 square miles which is twice the size of New York. Hampton Court Palace is 16 miles from the Tower of London for example, but there are 272 tube stations and 330 railway stations plus 9000 buses so you will be getting around. Use contactless to pay for your journeys.

Much as I hate to say it, I think you'll miss Highclere Castle. It generally has a spring opening in April, and is not open to the public in March. This is fairly typical for stately homes. As an alternative you may want to visit Hampton Court Palace, which is an easier trip from London, far more historic, and will be open.

Aside from what you have scheduled, maybe a museum? As a wartime history buff, I'd recommend the Imperial War Museum. Also perhaps a market? I like Camden Passage.

Covent Garden is a good central spot, but you'll still need to get a tube or bus - London is huge. I cant think of anywhere in London that tourists are likely to go that is not safe.

How exciting for you, Jay! It's been a number of years since we've been to London but spent a week and had a great time; there's SO much to see!

Personally? You might reconsider the trip to Highclere and take a look at Windsor Castle or Hampton Court instead? Neither are off tourist radar, and I've yet to do Hampton Court (next time) but Windsor was well worth the trip due to its long, long history. St. George's chapel, especially, is a fave. You could also walk over to Eton while you're there: The Eton Walkway look like fun!
https://www.windsor.gov.uk/things-to-do/the-eton-walkway-p1405401

https://ae6ab00e-2aa3-4774-be50-c07df9554132.filesusr.com/ugd/241361_4da7de0c7cc0402fa9a04b66efa13f1f.pdf

And I suppose we'd like at some point the Underground/Tube experience
as well.

That's pretty much mandatory for London as, per Trelawney, the city is very spread out and doesn't really have a compact historic center, per se, like Rome or Florence. It's comprised of individual towns and villages that were absorbed into the smaller, original city over a loooong period of time: urban sprawl, don'tcha know. We didn't find the Tube system to be difficult to figure out.

Not exactly off tourist radar but less visited is the Treasures Gallery in the British Library (also called the Sir John Ritblat Gallery). Free, and an excellent choice on a rainy day (and even a dry one). Yes, you will need to take the Tube or other transport to get here. Rick gives it a high-five too!

https://classroom.ricksteves.com/videos/treasure-of-the-british-library

London also has many small museums. Two of my favourites- Sir John Soane's Museum, which is filled with an incredible collection assembled by architect Sir John Soane and preserved in it's original form by Act of Parliament; and Leighton House (which is in Holland Park), the home of Victorian Painter Frederic Leighton.

You might also like Spencer House, in St James's overlooking Green Park. Built as the London home of Lord and Lady Spencer, it is quite magnificent and not particularly well known- it's open only on Sundays by guided tour, and when we went, only 3 other people were on the tour.