Haulover canal is nice and it's a well known spot and a good one. There are many places to wade fish within the Mosquito Lagoon Indian River Lagoon area that aren't muddy. They require local knowledge and I suggest you find someone who fishes there regularly and tag along. From there you can venture out.
Be warned, although you are in the National Park System, if you decide to go to some of the primitive ramps be careful not to leave any hint of valuables in your car. Just simply don't bring anything you can't afford to be without. Unfortunately there have been several vehicle breakins by some local vandels that as of yet haven't been caught.
Actually, on your way to Haulover there are a couple pull offs to the right. You can pull your car right up to the edge of the shore and wade out there.