For the absolute best Mexican I've found ANYWHERE try La Nortena over on Rivers Avenue. Traditional style everything - no order by numbers place. Besides the standard tacos/tortas/burritos (which are great), I particularly like the ceviche and (though I know this isn't fancy) the charro beans. Downtown there's also a place called Santi's that I don't rank quite as high as La Nortena, but they're still quite good as well.
For Thai I really like a place called Mei Thai which is in the same shopping center as the Ice Palace behind Northwoods Mall. Great Phad Thai, Fried Rice and curries.
BBQ: it's outside of Charleston directly, but I really like Music Man's BBQ in Moncks Corner.
Seafood: Again, outside of town, but Seawee Restaurant in Awendaw is amazing.
All very casual places (I'm not much for fancy - I'm more about how the food tastes), but all great.