I travel to London several times a year on business. I have recently begun tacking on a weekend after and taking the train to other places. My options this time are Edinburgh (i will be up at Cambridge, so only 4 hours or so), or over to Belgium or Amsterdam.
Thoughts?
I loved Glasgow even more than Edinburgh: The University of Glasgow is gorgeous, the cloisters, there is a cool museum (Hunterian) on the grounds; Kelvingrove Museum (the Dali painting is cool); Necropolis; Glasgow Cathedral; Ashton Rd, walking the west end. Very cool, much nicer than I expected.
Honestly, you can’t go wrong with either choice. Amsterdam is great – so much to see – and such a fun, youthful vibe. Then again, Brussels has chocolates & the pissing boy. I’d recommend choosing by alphabetical order 
I love Glasgow too. DH went there twice for conferences and I tagged along. I’ve been to Edinburgh, but have spent less time there and the last time I was there, my agenda was driven by a pre-teen son. Actually I love Scotland - hiking in Skye, Puffins on the north coast, stone circles in Orkney, Loch Lomand, Loch Ness. I’d go back in a heartbeat.
How about Bruges? It is a charming city. One of my favorites in Europe.
You asked about Edinburgh, Belgium or Amsterdam, not any other place, so I’m going to answer your question as asked. You have one weekend - three days, two nights, I assume - and for that I’d pick Edinburgh. It’s a city rather than a whole country (albeit, smallish countries), so you can really get a better feel for the whole of the place in a short time that way. Edinburgh is one of my favorite cities in the world.
Shetland. Well, maybe too far. I’d go there in a heartbeat.
No brainer - with only a short visit, transport time is best to Edinburgh direct from Cambridge. (I thought it was more like 5 hours by train than 4???) No need to back track to London to continue your journey. Save Amsterdam and Belgium for when you are starting from London. Walk the Royal Mile and stop in at Holyroodhouse if Her Majesty is not in residence.
"It’s a city rather than a whole country (albeit, smallish countries) "
Amsterdam is a city, too. 
While all are preferable in nice weather, Scotland will be the worst in bad weather if you are hoping to venture beyond the city. So I would do that one in summer.
I think Amsterdam could keep you the busiest, and I agree with @silverlady that tacking Bruges onto Brussels makes sense, so plan for a weekend when you can do both the B destinations.
My vote would be Edinburgh too. One of my favorite cities!
I loved Amsterdam when I visited. I was young and alone. I stayed in a hostel which provided breakfast. I took tours of Anne Frank’s house, the Heineken brewery, a canal boat ride and the jewelry district. On my own, I visited the Rijksmuseum, the Van Gogh museum and the Red light district (though I passed on the live shows). I also took a day tour to the Hague, Delft and another place that I can’t remember but it was like Legos. I had just a couple of days there and I had a blast. Of course, I was in my 20’s and could walk for miles and live on zero sleep. Even then, bicycles were plentiful but I actually don’t know how to ride and would never attempt to do so.
I haven’t been to Edinburgh, but now that H has discovered his family there (and one of the cousins has visited and stayed with us), it’s on my list.