Great comments here. Seems like most people are saying don't bother leaving London unless it's for Paris or maybe Edinburgh. I figured there'd be a lot of people here with experience in London that this would be a good thread to start.
How long will you be there? You can easily spend 1-2 weeks in London and not come close to running out of things to see.
If you're there longer, Bath is a great day trip. I'd skip Scotland and Paris for Dublin and other parts of Ireland if you're feeling truly adventurous. Simple train-ferry combo gets you there. Can't miss with the Guinness Brewery. The Book of Kells is pretty cool too. Plus, pubs and irish people.
Loosely assuming like 1 week total. I have been to Dublin and enjoyed it, but no real desire to go back there because I've seen a lot of the main sights just a few years ago.
There is nothing set in stone yet, I just kinda wanted to put feelers out to see what kind of things we could expect. I know London is a massive world-famous, Alpha city, but I had no idea there was so much to do just right there.
Seems like Paris could be an option for a short trip too, I knew it was close but didn't realize it was THAT close.