id be tempted to ride around Fylingdales, then head to Robin Hoods bay for a beer and then back along the old railway line (along the cliffs) back to Whitby.
You can always try cheeky routes around Goathland, Grosmont, Danby… or check out Rosedale (i hear there’s a bike centre there now). The bridleways around goathland, and the moorland, get very boggy when it rains, which is a shame because I think it’s great riding there.
If you do go to Goathland, try the route from behind to railway station to Darnholm, and then take that north to Whitby. There are lots of routes back to whitby, but they probably aren’t marked on a map. They’ll be used by the hunts, games keeps and so on…
When i was a kid, i’d ride from whitby to Falling Foss. Some nice riding there, though i don’t know whether it’s legal or not.