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Located in the heart of the Peak District National Park, high above the town of Castleton lies Peveril Castle. This Norman castle is owned by English Heritage so there is a charge if you want to climb to the top of the hill where it is strategically sited. That is, unless you are a member of English Heritage, in which case it is free. If you have sound legs and you can face the climb so the rocky outcrop where the castle is located, then you can get an amazing view over the some fantastic Peak District Scenery.
There are many other things to do in and around Castleton, which could be combined into an itinerary, as this attraction alone probably wouldn't merit a specific trip. On a busy weekend in the summer, it can also be difficult to find a parking space in Castleton, so either be prepared to park on the road outside the town and walk in, or visit one the caverns too, and pay for the use of their car park.