a taxi to Whitby from Robin Hood's Bay will cost about £9 or £10 so if you can find another couple to share the journey with it's not bad compared to the cost of parking (and petrol) and much less shredding on the nerves than trying to find a space :)

here's a link to the Arriva 93, X93 Scarborough to Middlesbrough timetable (it comes up showing Middlesbrough to Scarborough first) click on the 'current' tab to change it to the after April timetables and the 'return journey' tab then the + sign to get the times from Robin Hoods Bay into Whitby   :)