Johnny five,
Im going to take a stab at giving you some direction, as I am from jacksonville and lived there for 30 years. With that said, take my info with a grain of salt as I left town in 2008 and have mostly fished for bream and saltwater species on my visits home.
Ok so bank bass fishing in Jacksonville is all about ponds. There are literally thousands of them in Duval county and many of them hold very big bass. The trick is gaining access to the quality ones or at least not getting kicked out of the ones you aren't supposed to be fishing. Usually that means private property and neighborhood ponds. I would focus on those near J. Turner Butler Blvd on the south side and near the Town Center area. The development in that area over the past few decades has brought a ton of ponds that you can probably fish without drawing too much attention. The ponds in that area tend to be clear, shallow, and very grassy. Bluegill will be the primary forage, although ponds fed by creeks, while rare, will hold golden shiners as well.
If you have to fish public waters, the ponds at Hannah Park do hold 10 lb bass. That water is murky, green, and brackish (there are giant blue crabs in that lake), with lots of shoreline cover and some good timber around fish able banks. The pressure is high there, but you might be able to rent a kayak and do some good.
Speaking of renting a boat, you need to consider a few other options. First, I know for a fact you can rent a boat at NAS at the marina. They have some nice center consoles which you might be able to drive to doctors inlet. If you can, those docks should yield some fish on buzzbaits and 7.5 inch culprit worms. The worms do pretty well around the reed lines in Doctors inlet too. The second boat rental option to consider is if they have them available at Kingsley Lake south of Middleburg. The lake is 2 miles across with no public access, and military personnel accessing the lake from the adjacent Camp Blanding are some of the only people able to fish it. It is unusually deep for a Florida lake with depths nearing 100 feet and has yielded HUGE bass in recent years with light pressure. If you can find another service member to take you out or if they rent boats (which wouldn't surprise me), try drop shotting Junebug trick worms in 20-30 foot of water with grass over the summer.
If the rentals don't work out and you need further options, ask the guys at Arlington Bait and Tackle for suggestions. If all else fails just pick a pond and start slinging until somebody tells you to leave. Oh, and if you don't mind being an outlaw... Google this: "Sheelar Lake Gold Head". its the ultimate high risk high reward. lol
As far as lures, I used to like Baby Bass colored Flukes this time of year, although my PB (a 9.5 skinny post spawn fish) came on a Watermelon T-rigged Lizard in the middle of a hot April day. It was a 2 acre pond on the westside so don't overlook the tiny water down there. If you are chasing a trophy and don't mind live bait, try a bluegill under a bobber.
Hope this helps and sorry it's dated.