There are a couple of things that you can do. The first is to bring or rent a bike and pedal your way from lagoon to lagoon with your rod and a backpack or shoulder bag full of gear. I live on the mainland side of the bridge in Bluffton and that's what we do in the residential communities. You will not be able to park your car on the side of the road on most streets. If you do, security will eventually ask you to move the car.
You can rent bikes right in PD or have them delivered to where you are staying.
You can also rent kayaks and canoes right in palmetto Dunes and navigate the 12+ miles of interconnected lagoons. But I'm pretty sure that water is brackish and in there you will find red rum, sea trout, black drum, etc. If you want to fish for bass you'll need to fish the isolated lagoons. But to tell you the truth, I've never heard of bass being caught in PD.
There is good bass fishing in Hilton Head Plantation and Sea Pines Plantation. You can purchase a gate pass at Sea Pines and bring your bikes or rent bikes there. I have not fished there but only because I don't need the hassle of the traffic and tourists (sorry!) when I have better places to fish nearby. But I know folks that caught 5 and 6 pound bass in Sea Pines.
You can also bank fish at Jarvis Creek Park mid island. They have a concrete fishing pad and you can fish in some open areas along the shoreline as well. I fished there once and landed a few 3 pounders from the fishing pad. However, we encountered some aggressive alligators that day that crashed into the pad while we were on it. We got out of there and one of the bigger gators actually climbed onto the pad. This was a few years ago, but when it happened we contacted the town park manager and they sent someone to remove the bigger gators.
Off Island, near HWY 278 and i-95 is Sergeant Jasper Park. They have 8 or 9 lagoons there and many of them contain lily pads and laydowns. I fished there once at two of the lagoons near the main entrance and didn't catch much, but I plan to go back there again this spring. We'll bring our bikes because there is a lot of ground to cover to get to the more isolated lagoons. You can also rent canoes on the main body of water. This is a county park and an SC fishing license is not required, but there is a fishing fee that I think is $6.
If you know where you're staying be sure to check out Google Earth and look for the small, isolated lagoons in PD. The small lagoons here still hold some big bass.
One last thing - it's going to be hot in July. Brutally hot. And humid, especially in the early mornings. Be prepared for that. You also need to understand that no matter where you fish you will probably encounter alligators. Chances are they will not bother you, but some may react if you have a fish on the line. And before entering any area of dense vegetation or cover make sure you take a good look around, and keep scanning the water and along teh shoreline when you fish just to be safe.