I looked at the map just the other day actually. I think we can head down to Castle Howard via Coneysthorpe as Deano suggests, but if we want to avoid as much hilly stuff as possible (and I always do!), perhaps bypass Sherrif Hutton, and skirt through Thornton-le-Clay and Flaxton instead - on that route, it's pretty much flat once you drop down off the Castle Howard ridge. I've ridden it the other way a few times.
The only thing is that there are a couple of cattle grids - not bad ones, in fact the only ones I've been able to ride on on two wheels, despite my phobia. But easy enough to cross on foot if anyone is nervous of them.
Oh, I looked at work, and we don't have a suitable metal teapot, only a huge one. Bags in mugs I reckon.