When you say ride, do you mean dash to the destination or a leisurely jaunt ?
The Trans Pennine Trail will get you (almost) from your doorstep as far as Lymm, substantially free of main roads. It would include a short get off and walk soon after Dunford Bridge. From Lymm you could pick up NCN 5 to NorthWales.
Another branch ofthe TPT would get you right through Sheffield, via Conisbrough and Rotherham, you could reach Hathersage and find a way across the Peaks. Hathersage to Doncaster Station took me 4 1/2 hours recently, but every turn was GPS-flagged.