I buy meat and fish at the beach. For seafood, we are partial to Shrimpers, because we like the family who owns it. But all the seafood markets named in this thread are good.
Produce is another story. The Publix stores in the 30-A area are inconsistent in quality and don't have much variety. Depending on the time of year, the produce stands along the highways coming into Florida have good fruit and veggies, but in mid-summer most of what they have is not locally grown (exceptions are melons and sweet corn) If you care about produce, bring some with you.
I buy staples at the beach, they're the same price as home and I don't have space in the car for them. I do bring grits. The local Publix only has instant--yuk! If you like fancier pasta than they sell at Publix, check out the Modica Market in Seaside, which is also the source for lots of other fancy, yummy stuff for a splurge.
Speaking of splurging, Larder (midway between Seaside and Rosemary)has fabulous special cheeses and meat.
All the local wine and liquor stores are good. Best prices on beer and wine at Publix and Walmart.
Happy cooking!