Like Plow said, you really need a boat. In the areas where you are still permitted to fish, the bottom fishing is off the charts - mutton snapper are routinely the size of trashcan lids, a 10 lb. black grouper is ordinary, yellowtail snapper get to be a nuisance, and the 300+ pound goliath groupers will certainly test your manhood. Other regulars: tarpon, permit, giant barracauda, king mackerel, blackfin tuna... I could go on here.
Now about where you can and can't fish...
No fishing in the Tortugas Ecological Reserve (2 areas west and southwest of the park proper). Here is a link to a map that shows where they are:
No fishing in the Tortugas Research Natural Area. Here is a link to a map showing where it is:
http://www.nps.gov/drto/planyourvisit/u ... eprint.pdf
Tip of the day:
The area just to the northeast of the park boundary is where the shrimpers come early (and I mean EARLY) in the morning to clean out their catch. They anchor up and start tossing their bycatch over the side. WHAT A CHUMLINE!!!
I'm hoping to get out there this summer at some point.