Actually, many of the posters here urge that you see smaller towns, and not just concentrate on major cities!
In England, just a very few suggestions (not meant to be all-inclusive at all): Bath, Salisbury, Stratford, Oxford, Canterbury…
In France, the Normandy Region, Alsace, Burgundy, Loire Valley, Dordogne, Provence…
I think you get the idea—- there are so many wonderful places to go that it’s hard to pare down the list! Get a good guidebook or two and do some reading, and see what seems interesting to you, and then ask us more specific questions.
Many places don’t require use of a car, but if you can afford a car for a day or two, it may enhance your experience if you go to a region such as Alsace. In that region, you can easily take the train to major towns such as Strasbourg and Colmar. However, near Colmar, there are beautiful villages surrounded by vineyards, and roads up into the Vosges mountains.

I’d hit Normandy, Cinque Terre, Barcelona, Switzerland.