Well, York is in North Yorkshire, and flat as a pancake. You can actually do quite a lot within the Vale of York and the Vale of Pickering and down to Selby (straying in to South Yorks eventually) without a significant climb of any sort.
Allow an excursion into the East Riding, and you can avoid nasty lumps for miles and miles!
In fact you could go all the way to Hull.. But would you want to....