The Columbian - right on St. George Street, one of the oldest restaurants in Florida (the original one is in Tampa)
The Spanish Bakery - also right on St. George Street. It's wonderful!!! We go there at least once (& sometimes twice) a trip. It's a lovely, little authentic Spanish kitchen, & you eat on picnic tables outside. The empanadas are soooo good!
The Oasis - on A1A, fun little lunch place!
We also really like Barnacle Bill's (the one downtown - not the one on A1A) for lunch - very casual, simple seafood.
And Aunt Kate's on Vilano Beach is also nice & is on the water.
We also like Harry's which is across the street from the bay, but it's not really "traditional" St. Augustine.
A1A Aleworks is wonderful & gets consistent, rave reviews every year, but I'm not sure it's open for lunch. (The chef, I believe, is up for a James Beard award.)
Fiddler's Green used to be one of my favorite restaurants, but I'm not sure they're still open.
I think, though, if I were only going to St. Augustine for one day & wanted to eat in a restaurant w/ "atmosphere", I'd choose The Columbian!
Have fun!! We love St. Augustine! We go every year, & I always have a hard time deciding which place is my favorite - St. Augustine or Disney!!