I'm in Cheshire, so Alderley Edge gets my vote, especially as my dog just loves the place. Another would have to be Delamere Forest for it's swamps and dragonflies, and then a bit further on to Birkenhead, with the Dee estuary on one side and the Mersey on the other.
However, the lure of the peak district means is usually so strong that I don't often look around much more of the county. I'm a big fan of hills and woodland and Derbyshire definitely wins on both counts.