There are a few footpaths surrounding the site, with the nicest local walk being the 45 minutes or so to Linacre Reservoir, which runs via the Royal Oak pub at Old Brampton, if you need a stop on the way there or back. Otherwise, Chatsworth House (01246 565300) is the big local day out and it's an absolute treat — home to the grand Devonshire family and one of England's most magnificent stately homes and gardens. It's only five miles away to the west and it's an all-day visit, with everything from house tours and landscaped grounds to farmyard, woodland playground, estate farm shop, and several places to eat and drink.
The nearest market town is Chesterfield, five miles east, with its famous crooked spire on the Church of St Mary and All Saints (01246 206506) – climb it if you dare! The town's handsome enough, with quite a bit of historic interest, but in truth most day trips from the site are going to be to the west, where the gorgeous Peak District National Park (01629 816558) rolls across the peaks, crags, and moors between Sheffield and Manchester. For a bit more landed gentry grandeur, Haddon Hall (01629 812855) – about 11 miles away, beyond Chatsworth — is considered the most perfect example in England of a house surviving from medieval times, and there are intriguing tours of the house and parkland. Pretty, traditional Peak District villages like Bakewell get overrun in summer, so maybe think about running up to Eyam in the Hope Valley, about eight miles away. Known as the 'Plague Village', after the locals isolated themselves during the 17th-century plague outbreaks, it's at the heart of some excellent walking country.