Recommendation: call your congresscritters and complain bitterly about them allowing sequestration to occur and to continue for everything except their convenience (FAA).
Politics aside, Alpine or Swiss Inn are the closest things to Crabtree. Your other options are to try to get one of the (few) campsites at Mt. Mitchell state park, or Linville Falls. If you're headed south and want to camp, stay at Linville, then climb up and over Mitchell. You'll go downhill from Mitchell going down into Asheville, except for 3 miles climbing to warm up your legs, so that day will be 40 miles of mostly uphill, followed by an easy 20 mile coast down into the city.
Take lots of water. (Stop for ice cream at Little Switzerland.)