Lots of options for a gentle stroll or a longer hike. Open fields, rivers, woods, hills - Chatsworth Park has them all. On the down side, it's about 1 hr 45 minutes from Preston and there's a dogs on leads policy throughout the estate.
Our visit yesterday started out at Carlton Lees car park (it was free when we visited but there is now a charge for this car park on some days). From the car park, cross the road and head down to the river. In summer, this must be one of the busiest spots in Derbyshire, with kids paddling and adults basking in the sun. In winter, it's relatively quiet on week days but please observe the dogs on leads policy (our dog was not very impressed by the rule). Follow the river up to the bridge and then bear left and across the main road. Head up to the woods and back to Carlton Lees car park. This circular walk involves no stiles and takes about an hour and a half at a gentle pace. If you want refreshments take a trip over the bridge to the house or visit the cafe at Carlton Lees garden centre.
Lots of information is available on the Chatsworth web site
Doggy rating 5/10 (because of the dogs on leads policy)