If you like caves there are a number of caves you can visit in the Castleton/Edale area.. Treakcliff Cavern, Speedwell cavern, Blue John Cavern to name a few. Most of these caves are semi natural, in that there were caves there, but they have been expanded by mining for the unique to the area semi precious gemstone Blue John.

If you like stately homes, then Chatsworth House ( near Baslow) is a great example.

Bakewell (home of the Bakewell pudding), Buxton(home of Buxton water) are worth visiting- I love the Thai restaurant Simply Thai in Buxton

The village of Eyam is tragically famous because so many of its residents died in the plague of the 17th century

If you are interested in Industrial Heritage then go to Cromwell (near Matlock) as this was the site of one of Arkwright's first mills.

There's good walking in every direction- great views from Baslow Edge and Curbar edge, Dovedale is chocolate box scenery, and the Manifold valley has natural cave, Thor's cave- which is free to visit. My favourite walk is Lathkilldale from Monyash.

I hope you have a great time!