A bunch of good stuff is already above-I agree with about everything.
Little Bits for burgers, Bobs Hotdogs, but for most other eats I go to Southport. The Blue Water Point Marina / The Fish House Restaurant used to be pretty place if you wanted to stay on the island, but it closed. If it has been replaced, I haven't been back. I need to try some of those suggested above. Don't forget the two on the Fish Factory Road leaving the island toward 211-Rusty Hooks and Josephs Italian Bistro.
In Southport: Mr. Ps Bistro, Ports of Call, but my favorite is The Provision Company (Locals just call it "Provisions"). The 3 Crabcake Special and a pound of peel-n-eat shrimp is my usual order. This is the first April in a few years we are not going to start the spring there.
Southport is a great little town to walk the few shops. We also always (several times a trip usually) will take the ferry from Southport over to Ft Fisher (the battlefield is a great historical sight). The ocean side of 421 is also worth a look to enjoy. As stated, get a donut from Britts Donuts on the boardwalk if you are willing to fight parking and crowds (DEPENDING on when you are there.) They have a great selection of donuts (kidding-you will get a simple glazed donut and like it!) and a large selection of drinks (kidding-you'll get white milk in a Styrofoam cup, and like it!) You can of course go on up to Wilmington and see the USS North Carolina battleship, shop, find lots of restaurants, places to drink if that's your thing, etc.
We always hit the antique and consignment stores in OKI and SPT, and always drive over to the Orton Pond / Brunswick Town area. I love photographing the osprey and alligators at Orton Pond. There is a neat movie theather on the south side of 211 also we've taken some movies in at.