When I go to London, I usually stay at the Arran House Hotel. It's a few blocks from the British Museum. Last October, I only had 3 weeks notice and Arran House was full up so I stayed at the unfortunately named Beaver Hotel, which was fine, but not as conveniently located, though it's near the Underground.

I would definitely recommend the Tower and the British Museum. I've actually never done the Eye. Really must one of these days. (Assuming I can afford to get back to Europe sometime. Thank you, Scott Walker!)

I spent 2 nights in Edinburgh once, but my main memories are of meeting and getting to know a cousin. He took me on a drive by the Firth of Forth which was pretty. Oh, and an online friend took me to the Christmas market which was fun, but unlikely in July. On an earlier trip, a friend and I drove up to Loch Ness and then the Orkneys both of which I would highly recommend. Be aware though that the roads in northern Scotland are extremely narrow. Basically they're one car-width, but traffic goes both ways. It took us just about 2 full days to drive from Orkney to Cambridge. I think we rented our car through Hertz and they were fine. We picked up the car in Glasgow (after Worldcon 2005) and turned it in in Cambridge.

That's all I can think of that's relevant for now...