Do you particularly want to go to Wilmington? It's a nice NC city, but a better tourist destination from Asheville is Charleston SC and it's also closer. Nothing against Wilmington, but Charleston is pretty iconic.
Unfortunately not a whole lot worth stopping at between Asheville and Wilmington IMO. Maybe detour by Lexington NC for some barbecue? It's about a 5.5 hr drive between Asheville and Wilmington vs 4 hrs between Asheville and Charleston SC.
Wilmington is a great place to visit. If you're interested in history at all, you should tour the USS North Carolina Battleship Memorial. It's fascinating. There's also Ft. Fisher, and the NC Aquarium. Here's a link with lots of info:
It's a bit over 5 hours drive from Asheville to Wilmington. I would suggest taking I-40 to NC 16 to Charlotte, then NC 218 to US 74 (if you use google maps for directions, this is the second route option listed). Depending on what time you leave Asheville, you could stop for lunch in Charlotte. There are tons of great choices there, especially if you're willing to drive into the city. Or you could stop in one of several small towns along the way.
If you want to sample eastern North Carolina barbecue, try Smithfield's in Laurinburg. It's just off I-74 at exit 183. It's not the very best barbecue in the state, but it's a decent rendition of the regional style. The fried chicken is excellent too. It's not a fancy place, but the food is good.
You might like to do one night in Wilmington or Wrightsville Beach and then drive to Fort Fisher and take the ferry over to Southport for your second night. It's a small sailing port with lots of old houses and good restaurants. It's been the setting for at least one of those Nicholas Sparks books and movies. It would give you a different feel from either Wilmington or Charleston.
Sure. Southport is an easy day trip from Wilmington. Go to Carolina Beach and from there head past Kure Beach to Fort Fisher. The NC Aquarium is at Fort Fisher and is well done and worth a stop. You can explore the Fort as well (from the Civil War) and then take the ferry over to Southport. More info here:
Regarding JimT's comment above--the I-40 route through Winston-Salem and Raleigh is at least 30 minutes longer than the Charlotte route, and possibly longer if you hit Raleigh at the wrong time (traffic is brutal there from about 4:00 pm on). The Charlotte route takes advantage of the loop around the city, so you won't be in city traffic at all. And the NC 218 shortcut bypasses the traffic snarls in Monroe (plus it's a great scenic drive through the back country). Definitely a better route than I-40, unless you just have a desire to visit Winston-Salem or Raleigh.