I'd recommend going to some of the nicer restaurants for lunch, because everyone seems to charge about the same amount at lunchtime. I enjoy SNOB and Blossom for lunch, both have many meals available for around $8-12.
For dinner in the moderate range, definitely Hominy Grill, and I also like Virginia's on King. Both of those are Southern style.
Outside of downtown, you could go out to Sullivan's Island and go to Poe's or Home Team Barbecue (Home Team also has another location, in West Ashley). For burgers, Sesame in North Charleston is my favorite, and they just opened a new location at the mall in West Ashley. For affordable Italian, there's Mondo's, on James Island.
I think Al Di La is cheap if you don't drink wine. I had a app and small pasta the other night and the bill was $22 including tax and grat. Which is a good thing, 'cause the next night at Fig I picked up 3 veggies for the table and a bottle of wine + my entree and the bill was $113!
For moderately priced food...here are my recommendations:
Of course adult beverages pushes the $ over the top...
Triangle Char/Bar for great burgers
Dixie Supply and Baking - Tomato Pie and Shrimp/Grits - Breakfast and lunch only.
Pearlz - their chowder, gumbo and tuna burgers are consistently great
Mercato - on Market street. You'd think it be much pricier for the quality.