The United Kingdom is composed of 4 regions: England, whose capital is London, Scotland, whose capital is Edinburgh, Wales, whose capital is Cardiff and eventually, Northern Ireland, whose capital is Belfast.
Regarding England, I strongly recommend visiting London for a long weekend. It looks a bit basic, but you can never get bored there, whatever the weather. Other English towns, such as Bristol and Bath (both at less than 1hr from Cardiff) are a bit less popular, but they turn out to be quite interesting to visit. Bristol is actually a great base to visit the South-West of England and Wales.
Regarding Wales, I have so far only visited Cardiff. Cardiff Castle Heritage site and Cardiff Bay will be the unmissable elements of your visit.
If you're going up to Scotland, in the North of Britain, you'll be quickly pleased by its medieval capital, Edinburgh.
Eventually, if you would like to visit Northern Ireland, my website will allow you to discover all its counties. From my point of view, County Antrim and County Down (the most Protestant) turn out to be the most interesting to visit.
You will find below some links, which will allow you to see some photos of those 4 regions of United Kingdom...