Also, don't forget St Augustine. Conch House is on the water. They have little cabanas you can eat under. And, Caps in St Augustine. Both are outside and excellent.
Another good one at Jax Beaches I didn't see below: Giovanni's. I echo the comment about Casbah. This is a fun place to eat.
Thai Bistro in San Marco. They're under new management, so the prices have gone down a few bucks but most of the dishes are the same. Word of warning: the crispy spring rolls are not nearly as good as before. I was there recently and they were way too greasy. Also, the mango and sticky rice was definitely a miss.
Bistro Aix does great potato chips with blue cheese fondue. But for entrees, I prefer BBs on Hendricks Avenue.
Metro Diner. They made a great breakfast. Be prepared for a wait.
Chew. More upscale cuisine. I've enjoyed many a lunch there.
International Cafe. Open for lunch only. Small hole in the wall that makes a great cuban sandwich.
Burrito Gallery. Nice selection, better than the chains. Full bar and open evenings.
O'Brothers Irish Pub. Decent fish and chips if you can't get to The Prince of Wales in St. Augustine.
Mossfire Grill for Southwest cuisine.
Casbah is by far my favorite middle eastern restaurant in the city. I will admit to bias since they make their dishes just like my mom and grandmother did.
Blue Bamboo on Southside is a great for asian fusion.
I haven't been to 13 Gypsies as mentioned by another poster, but their sister restaurant Sangria House off Southside is very good.
Pattaya Thai & Lemongrass. Both decent thai places.
There are also about 5 Indian restaurants on Baymeadows alone. I enjoyed meals at Red Chilies and 5th Element.
A friend recommended Mandaloun for Lebanese. Haven't had a chance to eat there yet.
The Loop. Good for a burger and shake.
European Street. Great sandwiches and beer selection.
The many Ale Houses. Always busy, pretty good bar food.
That's all I can think of right now.
I was recently at 13 gypsies and loved, loved, loved it. Tiny place with only about 5 tables-including two outside, so I would call for reservations. Tapas place with the freshest ingredients and very reasonably priced. I live in CA and it is as good as many places in San Francisco in my opinion. I also like the Casbah, many folks like Bistro Aix. Not the foodiest of cities in my experience, but you can ferret out some fairly good places.
One thing you need to know is Jacksonville is very spread out, don't get frustrated though, there is plenty of good food. It really depends what you are looking for. Tento down in Jax Beach is a great Brazilian Steakhouse. Pussers in Ponte Vedra Beach right outside of Sawgrass is a nice Saturday afternoon outside spot. Fiann McCools in Jax Beach for Irish Pub. Bistro AIX in San Marco is always a good meal. For a good slice of pizza, hit Rennas at Town Center. BBQ is plenty down here, as well as seafood, too many too mention. If you narrow down your tastes a little bit, or your location, I might be able to point you in the right direction. Welcome to Jax.