In reply to jamesgreenfield:
I would also recommend further south, the roads around Hathersage are limited to mainly fast busy main roads. (I assume you're road biking?)
I cycle in the Hope Valley every weekend. The limestone areas are much quieter and more scenic. Look at the area between Buxton and Bakewell.
If you are still based at North Lees, you can keep out of Hope Valley if you head out on the Grindleford Road and out over Eyam, or up through Bradwell to the same area.