The Whitby road is one I'd put into the fast sweepers section. It's fun with good road surfaces but not really challenging at legal speeds. A good road to practice your observation/planning/overtaking skills on. It's usually our Good Friday ride out for fish and chips in Whitby. The road to Scarborough is better and worth the run out for the racing at Oliver's Mount. There's one particular corner on that road, almost a 90 deg left with a farmers gate on the opposite side of the road. The gate is a different colour every year as there's so many bikes have overshot the corner, gone through it and into the field!

The Weardale and Teesdale areas of County Durham are very underated as far as biking roads go. The maps often don't do the roads or scenery justice. You tend to get a lots of changes in elevation and camber through corners as you're right on the Pennines.

The B6277 is the road heading back over to Middleton from Alston. It scores 5/5 on Best Biking Roads.
It's ages since I've ridden the B6278. The section that runs between Stanhope and Barnard Castle is quite deserted apart from the sheep, depending on time of year. Tend to get wandering lambs running across the roads back to the flock at the sound of a bike or car.
The B6276 is another I haven't ridden for a while. Watch out for rabbits if you ride it at night. They tend to panic when they see your lights and run at your wheels. Gets a bit bumpy!

Durham England - Tourism in County Durham UK - Durham Hotels

The road from Melmerby in Cumbria up to the Hartside Cafe is a must if you're in the area.
http://www.multimap.com/s/0Hqe3jxQ

YouTube - up to hartside
Not exactly good riding but just to give you idea of what the road is like.