For years I've been making the treck all the way to Wrightsville Beach to go to Mott's Channel Seafood (about a 40 minute drive from NTB, but always fresh and worth it -- and I'm terribly picky), but lately I've been going to Surf City Crab in Surf City, and the shrimp has been great (I haven't yet tried the fish, but I hear very good things about them). They're just over the swing bridge on the island side, and right next to the Crab Pot Restaurant. It's kind of an open-air market on the sound, but the seafood is kept in coolers on a substantial bed of ice. Better storage conditions that 99% of the supermarkets in this area!
There may be fish opportunities on the island, but I haven't found them. Shrimp lady, a pickup truck and tent in North Topsail where Island Drive crosses the ICW and heads inland, has dependably provided excellent local shrimp for a number of years though.
I suspect the fish are in Snead's Ferry, but I haven't explored.