Me and Teatoosugars are both local to Northwich. IMHO, Chester is nice, Crewe, not so much, but like anywhere they both have there good and bad areas. Macc also nice and much closer to the peaks, where you might find a running club that suits. Not a runner myself, but there’s a Hash group in Northwich that some of my bike club mates run with. Frodsham is also a nice town and a bit closer than the areas you already thought of. Same applies for Tarporley.
Weaver Valley CC comes highly recommended, (as I’m the MTB secretary 😀 ) We try and have 2 rides a month off road, one in Delamere and one further afield, and there LOADS of road club runs if that kind of thing floats your boat. Other groups ride in the forest in the evenings mainly, but I’ve not gone out with them so not really sure where to point you. edit – Twelve50 cycles is a decent shop (Frodsham) and have a Tuesday night shop ride which is popular. edit 2, if you want to ride in Delamere, you’re really best of with a group or local(s) to start with as the good stuff isn’t marked.
And of course you’re in striking distance of the Monday Night Pub Rides in north Manchester too.