I used to live up in the area (hence the name)
It does get very busy at weekends, but as said earlier, if you get off the main routes it can be very quiet.
Castleton is an ideal base, very central, and you have the option of rugged moorland to one side up on Kinder (the lower reaches get very busy, but a mile further and it can be deserted.
the other way, there are gentle river valleys for very easy walking.
a lot of people will go out in the car, park up in a village and walk around the village, never going more than 100m from the car, visiting gift shops.....and that is their day out
Pubs in villages will get very busy at lunchtimes (especially on sunday) but could be almost deserted in the evening as people go back home.
Main villages with accomodation like Castleton will be busy all weekend.
However, if in the evening you go to a pub 'on it's own' then it will be quiet.
Prices will also be cheap compared to the 'rich' south, and portions are usually large
the weather can be variable, it may look sunny, but within an hour, it can be cold, and the rain torrrential.
Be careful if you are going up on the tops, as it is easy to become straded and losdt inpoor weather, and good kit is essential.
However, down in the valleys, this is less critical.
Use the Tourist offices, thety are very good, and will guide you to what you want, if my memmory serves me, there is one in Castleton.