The Camping and Caravanning Club site at Dunstan Hill between Embleton and Craster is great. I took the kids there a couple of weeks ago and going back next week (with the wife too this time).
It’s not too big and they space everyone out well so even when fully booked it doesn’t seem to busy. It has spotlessly clean loos and showers and very friendly staff. The pitches are very flat and not rocky too. There’s a couple of swings and a climbing frame/slide for kids plus as it’s fully enclosed the kids can go exploring. It’s only about 1/2 mile from a really lovely sandy beach – either on a footpath straight there of a quick drive if you have loads of stuff to carry down there.
The Cottage Inn http://www.cottageinnhotel.co.uk/ offer a minibus service from the campsite to the pub and back so you don’t have to drive (it’s only a couple of minutes drive away). You just ask for the service when you book a table.
Other pubs and a decent kids playground in Embleton.
I’ve used the Beadnell C&C site before and it tends to be very windy as it’s open with no cover and is next to a busy road. I wouldn’t bother with that one.
Procter Steads is ok but Dunstan Hill is nicer IMO.