It's a full life, if a trifle banal

Art in London: the National Gallery is one of the best in the world; the National Portrait Gallery is my favourite. And there's the British Museum. Those should keep you going for a while!

Leeds Castle is your best bet near London.

Cambridge doesn't really do castles, but the college buildings are well worth seeing! (This is King's College Chapel.)

And between us, Mr A. and I can certainly suggest some good eating places around London and Cambridge!