there are most definetly local mtns. (read big hills) i have climbed easily dozens of times and one atleast 100. although they are not remotely wilderness, there are close, quick and easy when only a few hours are to be had. and certainly better than staring at the idiot box.
nearby avon mtn. has some nice views and some sweet little spots to chill at and i must have climbed that thing a hundred times, whether hiking or trail running.
east peak castle craig was super popular for a group of us one summer, probably a few dozen night ascents before we got our car ticketed.
monadnock i must have hiked 30 or 40 times, its a fun mtn and i try to climb it monthly from sept to april or may. many many less people there in the off months.