Whitby's high season is the British school summer holidays, July and August, when the town can feel uncomfortably full. The shoulder months of May, June, and September give long days, mostly mild weather, and far less queuing for the chippy.
Two events justify their own visit: the spring and autumn Whitby Goth Weekends, and the Whitby Folk Week in late August, which fills almost every pub in town with traditional musicians. Winter is quiet, properly cold and grey, and atmospheric — the harbour wreathed in sea fret, gas lamps lit, plenty of cosy pubs. Many smaller museums and cafes close on weekdays from November to February, so check ahead.