There's so much in the Peak District it's a very rich tapestry, you won't be short of subject matter.
Go with a clear open mind, see what you like and you'll find more of the same or similar. If you go to somewhere like Chatsworth House, which is well worth a visit, you'll be amazed at the landscape, towns, villages, etc, that you'll have to pass through to get there. It's unique as an area.
There is or was a great OS guide book for the Peak District. I spent 5 days there with Fay Godwin about 30 years ago on a workshop, it was great fun - I knew the area well enough to be her guide as her car was really her camera case.
I'm sure my lad would love a day out in the Peak District, lots of of other doggie smells, it's only 90 mins to the northern parts from home, an hour to the southern parts.
Let us know when you plan to be there, we can meet up point you in the fight direction, that suits you . . . . . . .
Ian