The cliff above the east side is the obvious starting point: climb the 199 steps to St Mary's Church and the ruins of Whitby Abbey beyond. The graveyard, the abbey, and the view back over the harbour are exactly the scenes that Bram Stoker used for Dracula's arrival in England.
Down in the old town, the Captain Cook Memorial Museum is where the young Cook lodged as an apprentice. The eccentric Whitby Museum in Pannett Park keeps fossils, ship models, and the famous Hand of Glory. The town is also the historic centre of the Whitby jet industry — most of the small jewellery shops on Church Street and Sandgate sell the real thing.
Walk the piers and lighthouses out into the North Sea, watch the Swing Bridge open for fishing boats, and find the whalebone arch on the west cliff, framing the abbey from across the harbour. Twice a year the Whitby Goth Weekend turns the streets into a Victorian costume parade.