Now, you gothic/horror fiction fans out there may know this place as the setting for Bram Stoker's novel 'Dracula'.
I've been to Whitby three times so far (once with family, and twice on Drama trips) and I can safely say it's a must-see for those visiting Yorkshire. It's got a pretty good beach, numerous tourist attractions (The Whitby Abbey in particular) has some spectacular views from both hilltops and bridges alike, is home to some darn solid amusement arcades and also boasts wide selection of different stores including 'The Seafarer', a pop-culture shop, 'Meadow', a clothing/fashion store and 'Truly Scrumptious', probably the best milkshake bar I've ever been to in the UK (I'll never forget my first Battenburg shake).
Plus, tying into its association with Dracula, Whitby also remains a popular spot for gothic culture, with numerous stores selling gothic merchandise (e.g. Pandemonium) and music festival that happens twice every year called the 'Whitby Goth Weekend'.
Plus, it's pretty close to Robin Hood's Bay and Scarborough, two seaside towns that I also wholeheartedly reccomend you check out (Scarborough for its shopping/arcades and Robin Hood's Bay for its peaceful atmosphere and rural aesthetic.)
If I had to have one strike against Whitby, I'd say the Dracula Experience they have there is pretty sh*t (it's basically just a small walk-through museum deciated to the 1992 movie, except you don't really learn anything new). But considering everything else Whitby has going for it, that's a trivial complaint at best.