Shopping: Black Mountain Iron Works, Cherry Street Gallery, Chocolate Gems, Merry Wine Market... too many cool little shops to mention them all.
Hiking: Montreat has several well-marked trails (note that many are fairly strenuous). Old US-70, barricaded for 3 miles just past Ridgecrest, is a hike or bike down a road closed for 50 years. It runs above the RR tracks, includes great views including some of the RR tunnels, and is just really interesting to see what Mother Nature has done to reclaim road, pavement, and concrete over half a century. Further in are trails in Pisgah National Forest.
Putt-putt at Phil's BBQ, just south of town on Route 9 (good BBQ too).
Jog or fish at Lake Tomohawk
Lunch or dinner
If you want to buy liquor by the bottle you must do it at state-run ABC (Alcoholic Beverage Commission) stores rather than at a traditional liquor store. Beer and wine are available for purchase at most markets, grocery stores and gas stations. The alcohol laws of North Carolina prohibit the sale of alcohol after 2AM Monday through Saturday, and from 2AM until noon on Sundays.