Need help planning LAST MINUTE trip to Edinburgh, York, London

I don't think it's last-minute - I think you'll be fine. The only hiccup you may find is the May 27 bank holiday (see https://www.gov.uk/bank-holidays) where the hotels may be more expensive or booked. But you still have 2.5 months which is not unreasonable.

Have you been to any of these locations before or would all locations be new to you? What do you like to do (e.g. museums, food, culture, wine...)

You have a good amount of time to pull this off. Flying open jaw into Edinburgh and out of London is the way to go. My adult daughter is disabled (Williams Syndrome) - she is mobile but she gets tired easily and hills can be a problem. We just took the hill up to Edinburgh Castle slowly. We did not do any major hiking either because of her limitations. But we saw a lot of Scotland and loved it! We had a car, so that made it easy for us to get from point A to point B without having to lift luggage onto public transportation. However, I think you will be fine for what you want to do for this trip. From Edinburgh, I would suggest booking a small group tour https://www.rabbies.com. comes to mind. Return to Edinburgh and take the train to York. York is easy to get around - compact and flat in the central area. You could take a minibus tour to see some of the countryside (Moors and Dales) - not to be missed if you have time. Train to London. No need to fly between these locations. I use Booking.com for most of my accommodation choosing the free cancellation option. I do like B&B's for Scotland and York.

Margaret

You can pull this off. :) In Edinburgh, you can buy a day pass for the bus system which will save you many steps. We also used Uber when we visited most recently last June. Here's a city guide for access. And here's another interesting site for you to review. There are lots of other sites to explore if you google Edinburgh disabled access and quite a few come up.

You have lots of time for side trips and can take your time seeing Edinburgh. There are lots of easy day trips from Edinburgh: Glasgow, Stirling, St. Andrews, the Borders. You might want to search on tours. Rabbies Tours are popular, but I don't know how well they would accommodate you.

We have a similar limitation with hills and stairs. One thing we learned is not to be shy about asking people to please let us use the railing at places like Edinburgh Castle, where other tourists tend to congregate at the sides of stairways. Once they realize someone needs the railing, they're very kind about stepping aside.

Lodgings in Scotland tend not to have any rooms on the ground floor (something to do with damp chill, no doubt) so you may want to book a hotel with an elevator ("lift"). Remember that "first floor" means first floor above the ground floor, i.e. American second floor. We enjoyed the Inverleith Hotel and would happily stay there again -- especially because of the extraordinarily helpful staff -- but it does require climbing stairs. It is right around the corner from a bus stop. https://www.inverleithhotel.co.uk/

One side trip we enjoyed is Roslin Chapel, an easy half day from Edinburgh. If you buy a day pass on the bus, you can return to your hotel and freshen up, then use the pass again to go out for dinner. The Tower Restaurant in the National Museum is excellent, and if you time it right you can dine during sunset. The museum itself is huge -- a great place to get in out of the rain -- with exhibits for all different interests.

To get from Edinburgh to York, and onward to London, I'd take the train. You will get a better price on train tickets if you buy well in advance.

I have walking limitations myself as I suffer form Ehler's-Danlos syndrome. Last year we did almost your exact trip (but in reverse) and I had a full medical knee brace on one leg and a surgical walking boot on the other. I was able to do Edinburgh, by just taking my time and resting when I had to. One of the great things is that there are so many places to sit and have a quick drink while you rest. Using the HOHO Bus also helps too. Our favorite hotel in Edinburgh (we have been 3 times) is the Sheraton Grand. It is a great location - short walk to both New Town and Old Town and not that far from the train station either. For a little more money you can request a Castle View room, we could watch the fireworks over the Castle from our room (we were there in August for the festivals)

I hope you have a fantastic trip - York is one of our favorite cities in England.

May 23-24 Train to York (better to fly?) and visit there
May 25-29th Train or fly to London and time there

You cannot fly to or from York, much too short a distance. Train Edinburgh to York and York to London both take 2 hours. Suggesting flying such distances is proof of "not knowing the terrain".
Look up train times and buy tickets on the rail company's own website: https://www.lner.co.uk/

You can pull this together, you have over 2 months, plenty of time. For example Edinburgh to York on 23rd May is currently selling at £33.45, York to London on 25th May isn't even on sale yet (24th is "from" £38.50). Train prices never go down, only ever up.
To see in York: Minster (Cathedral), walls (with gates), lots of old streets. Museums, Clifford's tower, railway museum (but you only have 2 nights!).
From Edinburgh to York try to sit on the left for the best views.

There are plenty of side trips available from Edinburgh as mentioned. However, bear in mind Edinburgh is not particularly near the Highlands so it's not a good base or that well situated for taking trips there.

There are a few companies like rabbies and timberbush that do day trips from Edinburgh to the Highlands, but due to the distance be prepared for it being quite a long trip!