London is a great town. Tons of stuff to do, you'll never be bored. We took some day trips to surrounding areas... Stratford-upon-Avon, Windsor Castle, Dover, Cambridge.. You could even take the Chunnel into France for the day. Maybe take in a play or two.. I always felt safe walking around London, even at 1am just kinda wandering around with no particular place to go. Of all the places I've been to, London is probably my favorite place to visit. I'd go back in a heartbeat.
I loved Edinburgh. The castle is beautiful. Countryside around the town is beautiful. Nice little city.
I found Glasgow to be a rather boring place, from a tourist's perspective. Just an industrial city, not much touristy stuff to do.
Try to visit other places in Europe while you're across the pond. Madrid or Rome or Athens or Amsterdam or maybe even Paris (didn't really like Paris)...
