You MUST rent a car to see Wales. Also, I do drive the day of arrival from a transatlantic flight, BUT not very far. I suggest no more than two hours.
Also, you we did South Wales and England (not London or east of London) and spend 4 weeks.
Yes, don't keep your car in a major city. You can keep it in York if your hotel or B&B has parking.
Here is my detailed review of our self-driving tour of S. Wales and England.
28 days in Britain and Celebrity Eclipse home
For S. Wales, I recommend Cardiff, Tenby and St. David's (also see in link all the castles we visited).
We did five nights in S. Wales, 6 in the Cotswolds, 3 in York, 2 Durham, 1 Hadrian's Wall, 3 Lake District, 2 Winchester, 1 on our way to Whitby from York.
Edinburgh is better than Glasgow. Also, the area around St. Andrews north of Edinburgh. Inverness is in the far north and a bit of a trip, but great to see it and Loch Ness.