Park anywhere you like in Pickering. Taking an umbrella each, because it never stops raining in Whitby, get the free oldies bus to Whitby which is one of the most scenic bus routes in the UK, officially. There is a pre-recorded commentary as you drift along the countryside. Admire the driver's skills as he takes the bus along a route that you and I wouldn't take a campervan. It passes through Goathland which is the setting for Heartbeat where if you like you can get off and look around at the post office, scripp's garage, and the steam train station.
The bus passes Fylingdales anti-Russia spying station (AKA air traffic control for Europe) and you can spend the day in Whitby and have fish and chips at the officially best chip restaurant anywhere. After Whitby you can go on to Scarborough which is a dump. The reason for going there is the same as the reason for going to London. Every few years you have to go there to remind you of just how much of a dump the place is. Once in Scarborough you can cross the road and get the bus back to Pickering where you can stay more or less anywhere. But the road near the Castle, which is excellent, is wide enough near the castle to park but too narrow to park a motorhome closer to the town. If you are in EH of course, entry to the castle is free.
I have a vague recollection of staying a couple of nights in the Sports Centre car park in Pickering - no problems there at all.
