Not sure if Buxton is too far but Beech croft farm is a lovely site, tent field is great, dog walk is excellent, can let the dog off and the pubs not far either.
Lincolnshire, Smeatons Lakes...Newark on Trent...is that too far? lots of area to walk the walkable or bus into Newark.
Skegness water leisure park, just accross the road from the beach for the dog, pub on Site.
Check out Hutton le Hole caravan site theirs have a mile and a half walk, lots of waste bins and excellent views over the moors and a nice pub in the village.
enjoy
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Bainbridge in Hawes North Yorkshire 10 mins from site to town all brilliant walks. Every pub in Hawes welcomes dogs and food excellent.
There's the Wensleydale Cheese Factory and its ahem of a town.
You won't be disappointed and I would be surprised if you don't go back year after year. All the people that live there are all friendly and make you feel so welcome.
------------- It's nice to be important. But its more important to be nice.
Just back from a Certificated Site outside Lincoln £12 pn (but no shower). Loads of walks on paths beside fields in all directions, pub about 30 mins walk in the nearest village. Barff Farm. Similarly, no shower but dirt cheap and a massive field plus woods is the CS at Sutton Park near York, several pubs a few minutes walk away.
If you check the UKCS map search, tick the dog box, & anything else you need, and read a few reviews - someone will always write about the dog walk. That's the way we've found (or avoided) most of our 100+ dog-friendly sites for the last 10 years. The CSs are supposed to be for CCC members only, but we've never been asked and they are by far the best way to get away cheaply at high season.