Lots of very nice places on the Western side of London (easiest for LHR, although it isn't hideously hard to get to from anywhere).
I haven't spent much time in the Cotswolds but I will say Bath is worth a day of your time. Oxford is certainly worth an overnight stop, it is a bit twee but it has some beautiful buildings and fascinating museums. Be warned it is not a car friendly city.

Cornwall is beautiful but it is a bit of a trek (Paddington - Penzance by train is about 5 hours, I would be nervous about coming back on the day of your flight). If you want to go St Ives would be a good place to stay - quite a large town, lots of places to stay, pretty. There is/was a seasonal hop on- hop off bus service running a circular route between St Ives and Penzance which goes through some stunning scenery and past various historic sights. You could stop off overnight in Plymouth on the way back, a couple of hours closer to London and with far more trains. Or even in Exeter which isn't a major tourist destination but has a cathedral, remains of ancient city walls, and underground medieval passageways - and is another hour closer to London.

South Wales might be a possibility, 2-3 hours by train from Paddington. Cardiff is interesting, there's some beautiful scenery around Swansea and a great castle at Caerphilly.