Another from north Leeds here.
There’s a brilliant network of trails in and around the North/West suburbs, little pockets of woodland, twisty singletrack, some rocky/rooty XC-tech, some short, fun descents. I can be on the trails within 100m from my door, and TBH, that’s priceless; the ability to get out onto fun trails for anything from 20 minutes to 3 hours is just great.
There’s steeper off-piste stuff 40 minutes ride away (doesn’t hold up so well in the wet). Stainburn is 20 mins drive; Ilkley 30 (or ride out, train back). Long gravel/XC moorland half-full days are doable from the door. Calderdale, North Yorks Moors, northern Peaks all accessible within 1 hour 15 via train/car.
Riding (and, to a lesser extent, trail running) several times a week, usually 3-6 rides, is really important to me to get, even a quick (30-45 mins) fix of exercise fresh air, escape, reset, being in the woods, whatever the weather, and somewhere with decent access to that would absolutely be amongst the top priorities if moving.