Mount Pugh offers spectacular views when you emerge from the trees. There are lots of switchbacks, along with a very healthy scramble portion, and a walk along a ridgeline along which some hikers might meet with "vertigo". Your dog can make the hike (but needs to be leashed) because the trail has few obstacles and moderate traffic.
This hike is recommended only for very experienced hikers.
Mt. Pugh: 11.0 mi roundtrip
Elevation Gain: 5300 ft