Cadillac Mtn. Rock Climbing
First place that the sun hits in the US for some of the year (changes to other places depending on time of year/tilt of the earth).
Most folks drive up and hang out on the top, this is my suggestion since there is no worthwhile climbing route to the top.
Hike up, or use the convenient access road. Since you should get there before dawn, most folks (including climbers) use the access road so they don't have to wake up too early.
Weather station 8.1 miles from here
Featured Route For Cadillac Mtn.