Less than an hour's drive southest of Manchester lies the first British national park: the Peak District. This reserve may best be known for its limestone caverns and rock climbing options, but its relatively close proximity to urban dwellers certainly doesn't hurt the resume.
If you're content to stay above ground, there's plenty of hiking, mountain biking and horseback riding to be had throughout Peak District's scenic moorlands. For you subterranean types, however, why not opt for a little spelunking? Poole's Cavern in Buxton and the four show caves in Castleton are well worth checking out (Treak Cliff especially, because of its fluorspar content (a bright, crystalline mineral).
As far as rock climbing, there are a bevy of gritstone and limestone outcroppings that will pique your interest. Derbyshire's Windgather Rocks are a great starting point for beginners, while more experienced climbers will find The Roaches above the Tittesworth Reservoir to be to their liking. Refer to the included sites for more info on local caves and rock climbing sites.