Howick Hall: birthplace of Earl Grey tea (and purveyor of a very nice Welsh rarebit in the tea room!).
I've visited Howick Hall a couple of times, this last time a couple of years ago on a trip north with a few friends from London. We walked the gardens and then followed the trail out through the woods to the coast and a lovely deserted beach.
I'd highly recommend a visit and hope to go back before too long.