Frankly, a lot of the "attractions" at AB aren't there anymore--there used to be a fun "downtown" (known as "The Circle") with an amusement park, arcades, and, once upon a time, a dance hall. It was aging and, instead of upgrading it, they tore it down to build condos, just when the economy tanked. So now the "heart" of AB is empty land
Though I hear they are planning to rebuild some of the sorts of things that used to be there because people say there's not much to do in AB
Morehead City doesn't have a lot for visitors, though you'll want to go to the "waterfront" area (to the right after you cross the bridge) there to eat at least once. But do go to Beaufort, a historical town with its own waterfront and nice restaurants and shops. Kind of an "old New England" feel in some ways.
Also, past Beaufort there is Harker's Island, more historical stuff, sea museums, etc. Shackleford Banks is an uninhabited island that, I think you can take a ferry to for the day and probably see the wild horses that have just been "elected" NC's state horse (they date back to the 1700s or earlier and pirate ship days). There is also Cape Lookout, a lighthouse, reachable by ferry. NC's lighthouses are a state pride and you should see that one, for sure.
In the other direction, you have Swansboro which, like Beaufort, is another old sea town with some historic things and good restaurants. You'll pass through Salter Path (the heart of which is an old fishing village with GREAT fresh seafood) and Emerald Isle (which in the summer is jam-packed with traffic and tourists) but while you're down there, it's fun to explore the whole island.