You're always going to need your laptop. While it's true WiFi spots aren't as plentiful as in the US, they exist and you don't need to worry about some WiFi region rubbish. If you get a good adapter with an in-built transformer (and trust me they exist) then you can use this and your US power cable to get your laptop charged anywhere in England.
As for the places I recommend going: Cambridge (it's where I was at University!), Down House (Kent, the house of Charles Darwin), The Science and Natural History Museum (obviously), Bletchley Park, and if you don't mind the cost of the train ticket, Bath.