Two nights in London

Sorry to be the one to ask an obvious question, but what's "medium price" for you. To me that's about £200 a night, but your view on that may vary.

I can't think of a neighborhood or hotel in central London that's not safe.

Paddington, Bayswater, or Earl’s Court are good bets. They’re walkable, well connected, and generally easier on the wallet than staying right in central London.
Paddington is especially convenient with the Elizabeth Line from Heathrow, while Earl’s Court is on the Piccadilly line. Both are handy for a quick two-night stopover with bags. Of course, it really comes down to what kind of area you prefer staying in and what suits you best.

You might try booking.com. You can use it just for research and book direct.

Many members on this forum recommend Premier Inn (PI) which are all over London.

I will be staying in my first PI in London this October,

Thank you for your replies!
Medium price would be $150-250?
I don’t really enjoy chain hotels, I would rather have something smaller, more personable. I also REALLY enjoy a hearty Breakfast in England.

That's £110-£185- I do have a few recommendations.

Top of my list for your budget, and what I would call mid range, is the Thistle Holborn. It's quite nice, comfortable rooms, decent service. About £160 a night. Holborn is a lovely central area, and the hotel is close to the British Museum. Thistle is a chain, but this is a good property.

On more of a budget, basic level:

In Paddington (which I don't mind, but is arguably a bit run down and not the most central part of London), Mitre House Hotel (Sussex Gardens). Family owned, lovely staff. Tiny and basic rooms. About £120 a night. Used to stay there quite a lot.

Alternatively, there are LOTS of small budget hotels around Kings Cross station- the Alhambra in Argyle Street is about £110 a night. As long as you're ok with basic accomodation, it's fine. The Mitre House includes breakfast, I don't think the Alhambra does.

There are many other budget places around major stations, Paddington and Kings Cross in particular. And again, safety really isn't an issue in London.

Our last several stays in London have all been at Mike and Wendy’s bed and breakfast at 122 Great Titchfield Street. The name of the B&B is the same as its address. Very affordable (for downtown London), and in your price range, in the very safe and walkable Fitzrovia neighborhood, close to some outstanding restaurants, and Mike’s breakfast is outstanding, and cooked to order. They have three rooms, small, medium, and large, which are priced accordingly. Close to several Tube stations: Great Portland Street, Goodge Street, Oxford Circus, and the Dean Street entrance to Tottenham Court Road Station. Website: www.bb-london.co.uk .

That is quite a low budget for central London especially if you want to decent breakfast as well. You are probably better paying room only and getting breakfast elsewhere. Once you have accommodation sorted we can probably give some good food recommendations local to is area.

Everywhere in central. London is walkable and for longer distances you are never far from a bus stop or tube station. Is there anywhere in particular you are wanting to walk to or visit?

There are the two hostels, one in an excellent area near the Millenium Bridge and St Pauls. I bet the prices are closer to your very low limit.

https://www.yha.org.uk/hostel/yha-london-st-pauls

At a random two nights in November (you don't mention the actual dates) it is £20 per night in a shared room, toilet and bathroom down the hall or £160 per night for a room privately, toilet and bathroom down the hall. No en-suite available. Unlimited Continental breakfast included.

They have premium rooms, kitchenette and en-suite for more money, none available when I looked.

Your budget tends low for central London these days.

I’d like to take in the British Museum, a Victoria and Albert exhibit & possibly a West End show.

The British Museum and V and A are both on the Piccadilly tube line so it would make sense to stay in a hotel near that line especially as you are only staying for two nights. It also has the advantage of going direct to Heathrow.
You might have luck finding cheaper accommodation a bit further out west on the Piccadilly line, for example in Hammersmith and Ealing. If you can compromise with a chain hotel a few people on the forum have stayed at the Premier Inn in Hammersmith and seemed satisfied.

This hotel came to mind. I have not stayed there but someone on the forum wrote a review a few years ago:
https://community.ricksteves.com/travel-forum/england-reviews/the-celtic-hotel-in-london-comfort-and-convenience-at-145-per-night
I would suggest that you check recent reviews.

It is a good location near Russell Square which serves the Piccadilly Line. However, I’d suggest you check tube closures for the two days of your visit. The Piccadilly line has partial closures on a number of dates.
https://tfl.gov.uk/status-updates/major-works-and-events/piccadilly-line-upgrade

Sadly that is not a midprice budget but definitely puts you towards the cheaper end.

I agree with the suggestion of Celtic Hotel. In that same area (Bloomsbury - ideal for you) you could try the Imperial hotels. They’re a mini chain, not the small family style you might be looking for, but they’re respectable and clean and well-priced and get the job done: https://www.imperialhotels.co.uk/our-hotels/?gclsrc=aw.ds

Near Paddington (not my favourite area but safe and walkable and full cheaper hotels) you could look at the Darlington Hotel in Sussex Gardens. A bit further west, Vancouver Suites is very nice and friendly - but some of the upstairs rooms are up extremely steep flights of stairs.

The B&B I mentioned above is within walking distance to the British Museum - we’ve done that many times. It’s probably the closest major sight from the B&B, if you don’t count the Cartoon Museum :-)

It’s also walking distance to many West End theaters, and you could even reach the TKTS bargain ticket stand in Leicester Square on foot, although it’d be a longer walk. We took a double decker bus to and from the V&A; the TfL (Transport for London) App is fantastic for giving directions about how to get places by Tube and/or by bus.

Thank you all so much!