The Longshaw estate in Derbyshire is quite near Chatsworth and has excellent walking opportunities, even for the disabled, as some of the tracks are good for wheelchair use with views over much of the White Edge Moor.
Originally the Duke of Rutland's retreat it has fantastic views over the Peak District and the Derwent Valley.
It is worth visiting all year round, as there is a National Trust car park, cafe and shop, and the winter walks are as good as any other time of the year. It is free to visit, and can be very popular.