Nice and clean is priority.

There is a very simple, ie nothing there but a shower, near the entrance to Dalby forest at the Thorton le Dale end. I dont know how clean it is now as its a few years since i last stayed there, was very cheap though, £5 per tent!!
Think its called Moor Farm, great if your riding Dalby, there is also another in the centre of the forest but cannot remember the name, sorry.

the campsite at cropton forest is very nice and peacefull.

http://www.forestholidays.co.uk/camping_and_caravanning/our_sites__locations/england/spiers_house.aspx

try Vale of Pickering its predominantly caravans, but they have a ‘rally field’ that you can pitch tents on. Really clean, nice shower block and well stocked shop.

Good prices too.

Right in the middle of the forest is High Rigg farm
Just by the gates is Pexton Moor Farm