Not many boats go out of Jacksonville, and the ones that do are mostly about spearfishing.
Troy is ok. It’s a cone shaped hole that goes straight down to about 70 fsw, depending on the river level. No lights allowed, but don’t really need one. Viz is usually 30+. It’s better if you get there early, which is true everywhere, btw.
Troy is a state park, so it’s $6 to get in. Ginnie is private and it’s $30ish for mon-cave divers. Huge crowds this time of year.
My favorite cavern is Blue Grotto. It’s $44, but the biggest and most cave like. It’s big and open at the top, but you can go down to about 90fsw where it’s very cave like. You’ll need a light for that.
I have a 7mm farmer john which is good for cave dives because of the longer bottom times, but it’s overkill for cavern. I wear a 2mm shorty. I’m cold, but still prefer that over the 7mm.
Devil’s Den is an option too. Very close to Blue Grotto near Williston.