Waterside at Ruswarp is ace, eat outside it's lovely. Pricey but maybe do that for your birthday.
Pizza West is brilliant on Westcliffe. Very smart.
White Horse is classic pub food on the Abbey side in Whitby.
Ditto is great but strange opening times.
Check the Supper Club in Sleights - not been but great reviews.
Book for all.
Green Dragon and the Arch and Abbey for your ponce.
Abbey Brewery also good for a pint outside and great simple pizza.
I'm less clued up outside of Whitby. The pub at the bottom of Robins Hood bay is classic fare but pretty good for lunch.