i know what u mean, basically a field where kids can be kids and not worried about damaging the grass.
I've just check out Grouse & Claret Campsite
on AA route planner and from city center of shef it takes 37 mins and is only 20 miles.
I would personally recommend this site because:
- It has a great play area for kids,
- depending where everyone pitches their tents there is plenty of space for kids to play, me and niece were able to play Frisbee / football / and tennis with no problem (could be an issue if full)
- there is a river at the bottom of the site and kids can play it in, (its not that deep, but I didn't go all the way in)
- Nice pub on site to eat at / get drinks to take to your tent
- plenty to do near by, village of Bakewell, and Buxton
- plenty of nice walks to do,