Pannett Park museum is excellent (if you like museums) Ask to see the display case of the 'hand of glory'. It's a mummified human hand swiped from the corpse of a hanged man a couple of centuries ago. The hand of glory witches spell is fascinating and macabre is equal measure !
If you're in Whitby on a Saturday evening do the ghost walk. It starts from near Captain James Cook's statue at 7.30pm. No need to book, just pay five quid to the story teller who wears a black top hat with a black feather in it. (And is otherwise fully clothed !)
If you're a fan of Bram Stoker the author of Dracula, there's Whitby Abbey which was the inspiration for the story. (English Heritage wanted £8.50 per adult to look round. No thanks.)
Westcliffe, Whitby (about 25m from the Capt Cook statue.) There's a public bench that has not been altered since Victorian times - it's known as the Dracula bench.
Walk up the lane to the Church adjacent to the Abbey for great views of the Abbey and of Whitby and good sea views too.
Mr Moo's ice cream is delicious from an ice cream shop in the old town. Rhubarb and ginger ice cream was great.
'Mr Chips' does lovely evening food - proper meals not just fish and chips. Directly opposite is, 'Humble Pie' lovely pie and mash if you don't mind the 1940's décor in the café.
Pickering is described as the town that never was. However, the curd tart from the café was delicious.
Rosedale Abbey is a nice little village - not much there though.
Jet is a semi-precious gem stone popularised by Queen Victoria. Whitby jet is the best in the world - apparently.
Drive to Robin Hood's Bay and look around the village. Food in 'The Bay' hotel is lovely. Walk from there to Boggle Hole along the cliff top, it's about half a mile and there's a youth hostel at Boggle Hole where I think you can get refreshments.
You can walk along the beach at low tide. I was surprised to see an actual ice cream van on the beach selling ices. At 4pm he just drove up the slipway back into the village.