Thanks everyone for all the great suggestions. We shopped at Crosby's nearly every day and had many delicious meals using ingredients from there. We ended up having dinner at The Wreck. It was SO good and just the kind of place we had in mind. I loved the neighborhood it was located in, everyone was very friendly and not pretentious at all, and we really enjoyed ourselves. I will definitely be using this site again for finding good restaurants when we are traveling!
If you need suggestions for Asheville, let me know!
We'll be staying in Folly Beach next week and are looking for:
-a great, locally owned fresh seafood market. We will be cooking at home most of the time and want a great place the locals would go to.
-a great, locally owned seafood restaurant. We want something that's not too touristy, not all fried, not too fancy (we'll have our 2 year old with us), but not so kid-friendly that the food is no good. Someplace where you can get a lovely piece of local fish or a delicious local crab cake for $20-ish. Last time we had dinner in Charleston, we ended up in a too-touristy, fried place that served me a moldy lemon with my meal. Trying to avoid that!