Memorial Day Weekend in Charleston

I'm going to be in Charleston for Memorial Day weekend, covering the Spoleto Festival, which will keep me at the Gaillard Theater (my crash pad is about a mile away on Spring Street). I'm getting in on Friday night and leaving early Monday morning, which gives me two solid days of eating. I'm looking for some places to eat that will give me an experience unique to Charleston (I'm from New York so I'm not especially interested in things like Italian or Asian cuisine unless there's some wildly exciting thing going on). I won't have a car.

I was thinking of doing breakfasts at Bakehouse (which I know was originally affiliated with Baked in Brooklyn, but I'm not huge on breakfast so I'm just looking for a quick fuel-up) and Eli's Table and then balancing lunches and dinners between Cru Cafe, Closed 4 Business, FIG and Two Boroughs Larder. Does that seem like a well-rounded culinary tour of the area? Am I missing anything that would be a sin to ignore? And would y'all recommend reservations for all of the above places, or are there some where I can walk in without issue?

Also, on the non-food side, I'm wondering what I shouldn't miss in that general area to get a full taste of the Charleston experience. As I'm writing about Spoleto I want to get a genuine flavor for what Charleston itself is like as part of the article.

Also also, I'll be taking the train in (I know… but plane prices are stupid right now and I have a free travel voucher for Amtrak) and, as mentioned above, won't have a car. Are there normally cabs around the station that can take me over to my hotel?

Thanks in advance!