Ideas for trip finishing in Edinburgh. Looking at Glasgow and London

I would consider York and possibly Durham after Edinburgh. Both are easily reached by train from Edinburgh.

We spent two nights in York in June 2017, and could have stayed longer. We also had BritRail passes, for our entire stay (London, Bath (with day trip to Cardiff), Chipping Campden, York, and Edinburgh). They were not as handy as I thought they would be. To guarantee seats on trains you still needed to reserve (for an extra fee). Not worth it to us. You are better off buying train tickets individually as much in advance as you know your plans. On the other hand, the Oyster Card in London was a great deal for the week we spent there!

Anyone go to Glasgow?
Our Smart Tour does include York and Leeds are on Day 9. We thought we would see another city - therefore Glasgow.

It appears you have just 4 or 5 nights to spend since you need to be back down in/near London the night before you fly home (i.e., in London June 3). While you could spend that time in Scotland (and I do like easy-to-reach Glasgow), that's not a lot of time to see western Scotland, and most folks who go to Scotland really want to spend time in the Highlands/islands. If I were going to try that, I guess I'd spend every spare night on Skye rather than dividing the time up. But it looks awkward and exhausting to try to get from Skye to London in a single day. You can depart Kyle of Lochalsh at 6:11 AM and reach London at 5:51 PM, or you can depart Kyle at 12:08 PM and get to London at 11:32 PM. And it would be bad if one of your trains got canceled. In addition, tickets for those options are both priced at £196 (that's per person one way) for June 3.

Note: I did not explore bus options to see whether that would get you to Glasgow or Edinburgh faster and shorten the total length of the trip. There are lots of trains between Glasgow/Edinburgh and London. You could also look at flying from Inverness to one of the London airports.

Still, I'd recommend you plan to return to Scotland on a separate trip so you can get a more comprehensive look at the country. I'd probably head to York for 2 or 3 nights and spend the remaining nights in London. You could easily spend the entire extra time in London without running out of things to do, but York is very attractive and will keep you busy for 1-1/2 days or more. You could also spend all but the last night in York and take side-trips.

Edited to add re: Glasgow:
Lots of nice Victorian architecture. Interesting Charles Rennie Mackintosh architecture. Some good museums. Less really old stuff than in Edinburgh, I'd say.

If you are interested in seeing a bit of the Highlands in Scotland, you could do a short tour on a 16 passenger van with Rabbies:
https://www.rabbies.com/en/scotland-tours/from-edinburgh
A number of us have used and recommend them.

If you like cities, you can do a lot worse than to spend a few days in Glasgow. A few years ago, I spent four nights there, and didn't run out of things to do. It's a fascinating place with a unique energy, and as an added bonus, most sights are either free or low cost. On the other hand, it is very much an urban destination; if you want something more rustic, it won't suit you.

As for getting around, if you're going from Edinburgh to Glasgow to London, you'd want to take trains. This will be faster and cheaper than any other method. This is particularly true if you get Advance tickets. These are highly restricted discount train tickets; they go on sale about 11 weeks out, and you can only take the exact train departure you're ticketed for, and they're non-refundable, but in exchange for these restrictions, you can save a fortune.

If you want to learn how I spent time in Glasgow, Manchester, Liverpool, and Chester, here's my trip report: https://community.ricksteves.com/travel-forum/trip-reports/uk-trip-report-glasgow-manchester-liverpool-in-september-2016