I loved inland from Whitby for a few years as a kid (the second of my many accents) but it was a while ago and I can't remember which of the local delicacies I will have sampled.
My favourite place close to me is Hilbre Island, just off the coast of Wirral (Merseyside). When the tides are low you can walk out there, at high tide it's cut off. It's so close to Liverpool, and yet a world away. When I start walking from the beach towards it I feel like I'm leaving the world behind me and walking out into the wild. On a sunny day it's absolutely beautiful. It's a nature reserve and an SSSI, with loads of wild birds, butterflies etc, and there are small caves to explore at the beach level. It's one of my favourite places in the world.