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100% Dovetail! One of the best meals of my life.

Kanoyama!!!!! Get the omakase and you'll be blown away.

Il Cortile Del Re is AMAZING! So cute and romantic. They recently opened up a sister restaurant called Pane e Vino which is also fabulous and not too expensive. Pane also has a really cute outdoor space. I'd also suggest McCrady's (the chef is up for a James Beard award for best new chef), which is a molecular gastronomy restaurant.
Hands down my favorite restaurant in Charleston is Lana Restaurant. It's actually across the street from Hominy Grill and is not open on Sunday's. It's Mediterranean and consistently excellent. Really good espresso Martini's. Plus it's out of the way from the main part of downtown and is relatively unknown.
High Cotton has really good shrimp and grits, but I'd suggest only going there for brunch b/c it is really stuffy. And if you feel like waiting, Jestine's is actually worthwhile, but I agree that there is better out there. Oh and while I'm at it, Fleet Landing is right on the water and has excellent shrimp and grits. It is a little touristy, but you'll see dolphins over lunch and that alone is worth it.
And as for SNOB, I think there is much much much better out there. For basically the same (expensive) price you can hit up Peninsula Grill and get amazing service and even better food.
A really good place for a healthy lunch is called 5 Loaves Cafe. It's cheap, small, and it's definitely all locals.
Please avoid Hymans, it's truly a waste of time and money. I'd also say skip Rue De Jean, it's overrated.
Good luck and enjoy!
***An NYC foodie who spent 5 years in Charleston***

Anyone have recommendations on what kinds of mushrooms to use?

I like filet mignon. Yeah, yeah, its supposed to be not as good as other cuts, but taking a bite of melt-in-your-mouth rare filet is like taking a bite of heaven. Especially when paired with some sort of bleu cheese. Yum.