If you are staying in Carolina Beach, you should check out a bar called "Fat Pelican". Very unique atmosphere and probably the best microbrew selection on the island. In downtown Wilmington there is a beer bar called "Cape Fear Wine & Beer" that has the best micro selection in this part of the state.
Last I checked, Holly Shelter game lands still have the gates open. This would be a good option for a little off pavement action. Some areas in there can be either very wet, or very sandy depending on the weather, but the main drags in there should be passible even on road tires. Not for from Holly Shelter is a Road called "Old Maple Hill" and it's about the best thing in the area will will find as far as twisties go. Being from Ashville though, you will likely find it very tame. Mostly though, the roads in this area and strait with little to no elivation change. Not a riding paradise to be sure.
There is some decent hiking in Carolina Beach State Park. If you take the ferry over to Southport from Ft Fisher then take 133 north, you will find Brunswick Nature Park. There is some really nice multi-use trails in ther for hiking and cycling as well. There are a few dirt roads in there as well, but they don't go very far.
"Travel is fatal to prejudice, bigotry, and narrow-mindedness, and many of our people need it sorely on these accounts" -Mark Twain