Parking is a major problem in Whitby at the best of times. The official car parks fill up very quickly at normal times and they are very expensive. However, if you don't mind a bit of walking it's possible to find street parking not too far from the town centre. Another strategy is to find somewhere to park a mile or two from Whitby on a bus route, then go back at tea time and fetch your car in as the car parking charges come off after 6pm, though in these straightened times it wouldn't surprise me if Scarborough council have decided to extend the charges to 24/7.