Reasonable lodging in London & most scenic train service to Edinburgh

Premier Inn. All over London.

www.premierinn.com

There are lots in London. The Edinburgh train leaves from Kings Cross. So maybe look on the map on the website for those nearby. There seems to be one at Kings Cross and another at St Pancras (next to Kings X). Others at Euston.

That is a lot of sites to see in two days. (Are these two full days or are you counting your arrival date?) Windsor Castle is a day trip out of London and would occupy most of a day.

We plan on 2 full days in London.

Another vote for Premier Inns. County Hall and Waterloo are good locations.

Windsor is located out beyond Heathrow Airport, west of London. I think it will be difficult to accomplish all you want to see with only two nights in London. Two nights will give you only about 1-1/2 days there, and the first half-day may find you quite sleep-deprived and jetlagged. However, if you just want to walk past the exteriors of the key London sights you mentioned, it's probably doable; you could do that on your arrival day; walking around outside is a good way to fight jetlag. Then you could day trip to Windsor on your only full day in London.

Big Ben is being refurbished, so I don't think you can currently see it at all. I don't know when the work is expected to be completed.

One of the things you can do, if you plan ahead, is visit the inside of Buckingham Palace, a memorable experience and much more interesting than the better-known daily changing of the guard. The palace is open to the public, with advance timed ticketing, in August and September when the Queen is out of town.

I'm sure you know that London could easily fill a week or two if you had that much time. But the you could see the palace (inside) and Westminster Abbey in a day, Big Ben and the river are very close to the abbey. (Big Bend, on the other hand, is in Texas.) The RGS is also near the palace, with timed-entry tickets. So your two days would certainly allow you to see those places. You might look at the Premier Inn near Victoria Station which is close to them all and also to a major transportation hub with direct tube service to Kings Cross. (I haven't stayed there but I agree that the Premier Inns are a good chain.)

Windsor Castle is pretty much a day trip in itself. You could do that if you skip RGS.

Premier Inns are a good choice for London. I have stayed at the Premier Inn St Pancras twice. It is a five minute walk to Kings Cross.

We stayed at the Holiday Inn Southwark during our week in London. The location is terrific. Close to public transportation, sites, and restaurants.

Before we cancelled our trip we had settled on the area across from Big Ben, I think it's called County Hall? Several lodging options there, and a train station nearby which means you can always eat and shop if need be.

And you mention "train depot," hopefully you know that like Paris London is chockful of train stations. Some near each other, some not. Perhaps your train station should inform your choice of lodging.

I don't believe anyone has addressed the question about the most scenic route from London to Edinburgh. Most of the trains are operated by LNER and they take the fastest route, which passes through York, Durham, Newcastle, etc. No transfer is required. Running times are mostly 4-1/2 to 4-3/4 hours. There are a few Avanti and Lumo trains; they take an hour or so longer. I'm not sure what route they take, but with the Avantis departing from Euston Station (the others go from Kings Cross), I'd guess they don't follow exactly the same route.

I don't know whether the LNER route is more or less scenic than the Avanti route. You could of course cobble together your own route with a transfer somewhere, but it would certainly lengthen the journey.

British walk-up rail fares are among Europe's highest per mile. You can save a great deal of money by buying in advance. At a glance, tomorrow's LNER one-way fares seem to range from £44 to £183. Be careful about change and refund policies; none of us can be sure what COVID wrinkles we may face later in the year.

After two days we intend to travel by train to Edinburgh so will need
to get to the train depot.

A linguistical comment: In Europe, a train depot is a place where trains are parked when not in used, and also being maintained and cleaned etc. The place where passengers go to board a train to somewhere else is called a station.

Most of the trains are operated by LNER and they take the fastest
route, which passes through York, Durham, Newcastle, etc. No transfer
is required. Running times are mostly 4-1/2 to 4-3/4 hours. There are
a few Avanti and Lumo trains; they take an hour or so longer. I'm not
sure what route they take, but with the Avantis departing from Euston
Station (the others go from Kings Cross), I'd guess they don't follow
exactly the same route.

I can't answer the question as I've only used the East coast route from Kings Cross. But it is in my opinion scenic enough so that it's not worth considering the West coast route from Euston.

If scenery is the big concern, built the Settle to Carlisle into the journey, nothing comes close in England.
You would do London to Leeds to connect to the Settle and Carlisle

The Avanti route from Euston uses the West Coast Main line via the West Midlands and then north via Crewe. It climbs up to Shap Fell on the eastern edge of the Lake District and after crossing the border into Scotland near Carlisle climbs over Beattock Summit.
West Coast Main Line is a bit of misnomer as only glimpse of the sea is around Lancaster.
This route is a bit more scenic than the East Coast route
If you are doing a round trip you can always go one way and return the other
Suggest you consult www.seat61.com for information on rail travel in UK including how to book tickets from abroad

This train looks interesting. A sleeper....true not much scenery

https://www.seat61.com/sleeper-to-scotland.htm#trains

we just did the Lner train Edinburgh-London last week. Very comfortable. 4.5 hours to Kings Cross. Nice, clean & not crowded

In London we stayed at Hub by Premier by St James tube station. We liked the location a lot. A few blocks to Westminster, Big Ben. Probably 15-20 mins walk to Buckingham Palace/Hyde park. Tube station half block away. Victoria Station a few blocks

M61 is well up on the various London-Edinburgh options, and has videos, as do many other train vloggers.

The two main routes from London to Edinburgh have the names of East Coast Main Line and West Coast Main Line. Referring to them by the name of the long distance company who are currently running on them is easy - such as Avanti West Coast or LNER but these names change fairly regularly - remember Virgin West Coast and Virgin East Coast? - when the franchise or government agency decides to have another go at a name, or after an embarrassing incident or when a franchise changes hands.

And then there are the smaller or shorter distance operators such as lumo which go basically the same route as LNER but less frequently and much much cheaper, and London Northwestern Railway which cover the same ground as Avanti West Coast from London as far north as Liverpool - then there's Scotrail.

Perhaps better to refer to the route. The West Coast Main Line has branches but the fast part is London Euston > Watford Junction (Harry Potter Studios) > Milton Keynes (Bletchley Park) > Rugby (where the game was created) (and a branch to Coventry, Birmingham, Wolverton for connections to Shrewsbury and Wales) > Stafford (and a branch to Stoke-on-Trent (pottery) and Manchester) > Crewe (trains go from Crewe to everywhere - no, really) (branch to Runcorn and Liverpool) > Oxenholme (Lake District) > Carlisle > Glasgow > Edinburgh. So plenty of lovely scenery, no seaside, plenty of industrial too.

The East Coast Main Line is much straighter and therefore somewhat faster. London Kings Cross > Peterborough > Doncaster > York > Darlington > Durham > Newcastle upon Tyne > Edinburgh.

Plenty of connections are available off both main lines and there are lots of train companies running trains in all directions off both.

While the ECML does not skirt the Lake District it does provide a few views of the North Sea.

I think that the experience would be quite different...

Which is better? dunno. I worked decades on the West Coast Main Line (and branches) and am loyal but wouldn't want to say which is better...

I just returned from Edinburgh this morning on the overnight sleeper to London (Caledonia). On the way up it was very beautiful, but if I had it to do over again this time of year, I would leave earlier. My noon train from King's Cross was nice, but by the time I was getting to the pretty Scottish seashore, it was starting to get dark. Very different if you are traveling in Summer I guess. But if you take this route, be sure you get seats on the right side of the train if you want to see the best sights.

On the way back, I used the sleeper. I enjoyed it but of course you don't get a view. At seat61's recommendation (https://www.seat61.com/sleeper-to-scotland.htm) I went to the diner car shortly after boarding and before we left the station to get a seat (I was traveling on a Friday night). Afterwards I went to my cabin and tried to get some sleep (difficult if there are noisy people in the adjacent cabin). 45 minutes before scheduled arrival, the train stopped. I assumed it was a scheduled stop so I just got up, showered and ate. Only when I was done did I realize we had arrived in Euston early. All was good, but I guess my point is there isn't a lot of time to eat dinner, sleep, and also eat breakfast.