I addressed this a while back since I lived in Charleston for almost 10 years, so I'll repost. There will be a lot of recommendations for Jestine's, McCrady's and Slightly North of Broad, so I'll just add my 2 cents are far as off the beaten path places that locals enjoy.
Close to Isle of Palms you have The Old Village Post House:
http://www.mavericksouthernkitchens.com ... ation.html
It is part of the Maverick group which includes SNOB and High Cotton.
For some more casual, local places I would suggest:
Poe's Tavern:
http://www.poestavern.com/ - great burgers-they grind their own meat.
Gaulart & Maliclet (the locals call it Fast and French):
http://www.fastandfrench.org/G&M/G&M_index.html - Their seating is community-style, so you have to be prepared to eat with strangers, but I think it's a great way for tourist to meet and talk with the locals.
Sermet's:
http://www.americascuisine.com/charlest ... corner.htm - great food and atmosphere, perfect for people watching.
Pane E Vino:
http://www.charlestoncitypaper.com/gyro ... oid%3A9891 - wonderful wine bar. The owner is Italian and they do great authentic Italian dishes.
Have fun in the Lowcountry
