On the way down you'll pass two Morris Family farmstands. I'd recommend picking up both fresh seasonal produce, and some of their specialized canned goods.
My mind is melting, and I don't recall the name, but a block or so past the second Morris, on the left, is a seafood place. Great selection, fresh seafood, and reasonably priced. I'll check with Friend Wife when she gets home; I'm sure she remembers the name of it. But we always stop there and stock up for the first couple of days anyway.
When you cross the bridge to OBX there's a seafood market right there (assuming you're heading south), near the Walmart. Skip it. They have high prices and low quality.
Oddly enough, the seafood counters at the supermarkets are pretty good. We usually shop Harris Teeter while on OBX, but there are regular chains as well.
We're usually fishing and crabbing when we visit, so a lot of our seafood comes right from the water to the pan.