Ebbor Gorge (take a backpack containing some rope, refreshment, helmet and light - just in case
)
Any of the old Mendip quarries (similarly equipped as above)
The North scarp of Crook Peak (including the woodland) overlooking Compton Bishop (ditto)
Sandford Hill (ditto)
Brockley Combe (but you'll probably wish you'd taken SRT kit!) - thanks to Axbridgecaver for introducing me to this fascinating place
Banwell Hill (old follies and othersuch)
Axbridge Hill up to Chardswell Cavern searching and locating Ochre Mine, Triple H Cave etc. en route
Rose Wood - just for the exercise! - to visit the workings there
Rowberrow "forest" - finding the cavern in the woods is a good test, plus the cairns, the derelict house etc..
Brent Knoll - amazing archaeology and stunning views on a clear day - an easy(ish) walk (OK, so it's NOT MENDIP, but it's pretty close! - albeit, not walking distance).
Crook Peak - similar but MUCH WINDIER!
Cheddar Gorge "off route" adventurous danger-walks - up Chute Gully, head north, abseiling to Brock Hole and then down towards Black Rock following the scarps, attempting to locate the infamous Pant-y-Crack!
Cheddar Gorge, east side: locating Bone Hole (handline useful) then continue up onto the ridge for the stunning views of Cheddar Gorge and cutting back across via Piney Sleight to pick up Longwood path etc..
Draycott Sleights - to visit the caves and the karst and for the views and archaeology
Middle Down Drove - an interesting and "forgotten" part of Mendip!
err, that's enough for the mo......