Ladybower, Derwent & Howden Reservoirs has a great cycling and walking paths. There is a spectacular scenery as the reservoirs are surrounded by the forest. The cycling trek around all 3 reservoirs is 20miles, not hilly pleasant cycle. We have been there twice before but would be happy to return there any time.
Afternoon we spent at the Faggott village festival, where we saw the largest vegetables ever. I wonder if they were organic?
Another good cycling and walking trek is near Hassop, this is old railway track that now has been converted into walking/cycling trek. 4 miles before the end is Monsal wih the nice coffee shop and spectacular view. To get there park behind bookshop (A6020 and B6001).
Gritstone Edge is spectacular easy 7 mile walk (not good for cycling). Wide expanses of moorland with interesting rock formations.
Chatsworth House is definitely worth stopping and visiting. It's house of the Duke of Devonshire, belonging to his family since XVI century. It's surrounded by gardens, fronted by the River Derwent and backed by a tree-covered hillside. This time we concentrated on the sightseeing outside, early morning run (Mike run, myself pedalling) around the grounds was enjoyable.