Hi nannie!
I don't know what sort of distance you're up to, but it would be worth getting the
Ordnance Survey landranger map for Hull (map number 107, you should find that a big branch of Smiths has them in the book section). The most recent edition has the Transpennine trail, Route 65, marked on it. That will take to north east to Hornsea. I've not ridden it myself, but it'll be pretty flat, and looks to be off road a lot (anyone able to comment on the surfacing?).
Hang on, how stupid am I, of course I've ridden it. It rained....
Perfectly suitable surface for a Karakum, I handled it on a much skinner road bike, until I started to dissolve.
Invest in the map to the west, 106, and you can follow the route westwards too, along the Humber, and up to Howden and beyond. And you can also cycle over the Humber Bridge and back, which is fun.
Keep an eye on the Informal Rides section, we Yorkies and East Yorkies try and get together frequently for a jaunt, and we're very sociable and fond of cafes....