Depends on the route you plan to take. If it's ferries to Cedar Island, the first possible stop is 100 yards off the ferry at the Pirates Chest restaurant at the Driftwood Motel.
Very good local seafood. It's about the time of the year when they're only open weekends, however.
If you're going to drive around the Pamlico and Neuse rivers, there's Georgie's Sports and Oyster Bar in Belhaven. Maybe the best scallops I've ever eaten. Dinner only. The waterfront in Belhaven is lovely, but other parts of town seem to be hurting. Bath would probably be a better place for shopping. I don't know Washington or New Bern well.
Lots of good choices for food and shopping in Beaufort, although I'm partial to Beaufort Grocery Co.:
Beaufort Grocery Co
117 Queen St, Beaufort, NC 28516
Moore's BBQ in New Bern is a good place for BBQ. If you detour to Greenville, NC B's BBQ is also good. Washington, NC is a neat town on the Pamlico River with outstanding restaurants and shops in the historic water front district. Here's a link to shopping there. My son was a Marine at Camp Lejeune. We visited the Outer Banks several times and passed through Washington, NC on the way. It's a fun place to visit.
Moore's Old Tyme BBQ @ 3621 Dr. Martin Luther King, Jr., Blvd., New Bern, NC. 252 - 638 - 3937.
B's BBQ @ 751 B's Barbecue Rd., Greenville, NC. 252 - 758 - 7126.
Front Street Grill is very nice for lunch or dinner in Beaufort, NC.
Front St. Grill @ 300 Front St., Beaufort, NC 252 728 - 3118.