Let's head for the roundhouse; they can't corner us there!
The closest trailhead---which I assume you mean road access---would be in Big Fat Gap where the Big Fat trail drops down 1,500 feet in 1.5 miles to access the bottom start of the Nutbuster trail.
The other would be Wolf Laurel road which quickly accesses Stratton Ridge trail up to the BMT and then down to Naked Ground Gap and the top Nut trailhead.