This isn't directly responsive to your post, and you should of course feel free to ignore it, but if your itinerary is still wide open, here are a couple of things you might want to consider:
1) London is fabulous, but it's crazy to try to see it in a very short time. So unless you were going to spend several days there (which it's pretty clear you're not), I'd skip it altogether and save it for another trip.
2) Consider Wales. The Welsh countryside, and Welsh seacoast, is magnificent. Hay-on-Wye is enthralling and has the largest concentration of used bookstores in the world. The Gower Peninsula is magnificent, with many opportunities for hikes of all degrees of difficulty, all rewarded with stunning views. Hiking out to the end of Worm's Head (at Rhosilli) is one of the most awesome things you'll ever do. (And if you're a Dylan Thomas fan, it will be all the more meaningful.) There are forests, mountains, abbeys and castles galore. And Portmeirion is all a certain kind of geek could possibly hope for.
3) Hike the Cotswolds. There are several standard Cotswold walks, all of them beautiful, and all through countryside that is quinetessentially British, with all the thatched roofs and sheep and rolling hills you could hope for.
4) Bath rocks.
5) York rocks beyond all rocking. Like London, you shouldn't try to do it in a day, but you might be able to do a bunch of it in two or three. You can walk the perimeter of the city on the old medieval walls where the Yorkist's heads were displayed. You've got all those twisty narrow winding streets full of surprises to explore. There is activity everywhere --- amazing shopping, cafes, and, everywhere you look, the best street performers in the world.
6) In Scotland, the Trossachs are amazing. Loch Lomond is one of the most beautiful sights I've ever seen.
I have a gazillion more UK suggestions. Let me know if you want more.
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1) London is fabulous, but it's crazy to try to see it in a very short time. So unless you were going to spend several days there (which it's pretty clear you're not), I'd skip it altogether and save it for another trip.
2) Consider Wales. The Welsh countryside, and Welsh seacoast, is magnificent. Hay-on-Wye is enthralling and has the largest concentration of used bookstores in the world. The Gower Peninsula is magnificent, with many opportunities for hikes of all degrees of difficulty, all rewarded with stunning views. Hiking out to the end of Worm's Head (at Rhosilli) is one of the most awesome things you'll ever do. (And if you're a Dylan Thomas fan, it will be all the more meaningful.) There are forests, mountains, abbeys and castles galore. And Portmeirion is all a certain kind of geek could possibly hope for.
3) Hike the Cotswolds. There are several standard Cotswold walks, all of them beautiful, and all through countryside that is quinetessentially British, with all the thatched roofs and sheep and rolling hills you could hope for.
4) Bath rocks.
5) York rocks beyond all rocking. Like London, you shouldn't try to do it in a day, but you might be able to do a bunch of it in two or three. You can walk the perimeter of the city on the old medieval walls where the Yorkist's heads were displayed. You've got all those twisty narrow winding streets full of surprises to explore. There is activity everywhere --- amazing shopping, cafes, and, everywhere you look, the best street performers in the world.
6) In Scotland, the Trossachs are amazing. Loch Lomond is one of the most beautiful sights I've ever seen.
I have a gazillion more UK suggestions. Let me know if you want more.