I live about 20 mins drive from there.
Its a nice place but expect it to be busy, especially if its a nice day.
You can get some really good shots of the house from the surrounding parkland. Have a crack at the water fountain if its running.
If you walk along the river (downstream) there is an old derelict mill about 3/4 of a mile away, also a couple of weirs.
If you are in the area you could also try Bakewell and Ashford-in-the-Water. There are also some great shots from Monsal Head (and a nice pub) All within easy driving of Chatsworth.