I'd better join in this topic...
I second most of what's been said so far, especially oak's initial introduction piece.
It's also very true that London is not representative of the UK. I feel like it's almost a different country, like the old "city states" of Italy. I feel more Londoner than Brit, really!
I won't have Cambridge placed below Oxford
- you must have missed the best parts! OK, I'm biased, having spent 3 years studying there
. It's much more a University with a town, whereas Oxford is a real town with a University running through it.
Punting to Grantchester from Cambridge (by "The Mill") on a summer afternoon and having a cream tea in the same orchard of which Rupert Brooke wrote:
is SIMPLY SUBLIME!!!
Ideally you'll have consumed a couple of pints of Pimms on your way there and will just drift through the rest of the day!
Other highlights of Cambridge are the views of King's College from the Backs (the river side). Clare College gardens are delightful. Either St. John's or King's College Choirs are world famous and sing at chapel services.
The Fitzwilliam Museum has a strange variety of pieces, including a large number of original William Blake illustrations.
There are also enough decent pubs: from memory of 10 years ago, The Mill and the Baron of Beef are worth a visit for the beers and atmosphere.
I'll have a think about non-obvious London and post at items occur to me. KP