Any tips on sights and things to do on a trip to England, Scotland, and possibly Ireland?

kanman5000 asked: I will hopefully travel in early July for 2 weeks on a budget of $2000. Can anyone recommend cheap and fun things to do in London, Birmingham, Glasgow, Edinburgh, and Dublin? And any other places or things I should see/do while I’m in the area?
At the moment, the only must-see things on my [...]