The A169 Pickering to Whitby is the obvious one across the moors. I did this a few weeks back and enjoyed the ride. Turned out there was a massive steam rally on at pickering, not every day you get stuck behind a traction engine! Pickering looked a nice enough little town/village (don't they all int he sunshine?) although I didn't stop due to crowds.
If you're interested in visiting towns then Whitby is certainly worth an hour or two's exploring. There's a cafe frequented by biker's right in the centre of town next to Morrisons, and the town is famous for it's fantastic fish and chips and for the ruined abbey on top of the hill (and also a great YHA right next door!). Gets fairly lively weekend evenings due to Northern monkeys
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After staying the night in Whitby I headed home towards the midlands via the A171 (not a bad road) and Scarborough. Again, nice little sea side town with a friendly biker's cafe right on the sea front. Can sit out front by the sea and everyone is very friendly. Was the owner and local instructors there when I visited, nice folks.
Other than these two roads I don't have any further info, one of my least visited parts of the country so I'd be interested to hear of an other good ones too. Can take the A66 and be in the lakes pretty quickly if you fancy.
Andy