Hi There Grizzly Kelt, I have the same problem and live in east Riding near Driffield .When I'm in the local area most land is private especially woodland.
My local area is a good place for plant id and Tracking Deer,Badger e.t.c
Usually the land that is available is camped on by caravans and not very nice (rubbish bags etc)
I find the best place for me has to be Trouts Dale ,Broxa or Dalby Forest.. Pine,Birch (My Favourite Trees)dominate the area in North Yorkshire about 40 mins away.
Overnight camping in these areas is not alowed nor is lighting fires, I tend to spend the odd days there Harvesting wood ant nests gathering Cattails, Tapping birch or making Nettle Cordage depending on what time of year...
An uptodate O.S Map for your area will also feature some good walks
For anymore info just give us a shout................Gaz