When I visit the parents I'm based in Strensall , just north of York so it seemed to make sense to head northish towards Castle Howard etc but looking on the OS it seemed quite tricky to link a route together that was pretty road free.
I just wondered if there is some hidden singletrack heaven or classic loop that I'm missing...
Strensall Common is fine for an hour or so but it's flat (and boggy and the army shoot at you some days!).
Fyton/Slingsby just south of them (across the road and up the hill, you'll see a stretch of ) is a Signed cycle way, off road and plenty of routes off it. Walk a part of it while on holiday up there in the summer (though very boggy as it chucked it down
Seems to be plenty of routes of that main track. and if you go across the B1257 there are some simple bridleways to ride down (and pubs in the villages)
South you have Castle Howard
That about all I know.