Boo! Are you scared, yet? Based on the responses above, you would think that St. Augustine is the most in-hospitable places around especially for MD'ing. Don't believe the hype. As you know, by coming in the fall, you won't need a beach pass to drive. You still need to observe traffic patterns and speed limits, though, as the beaches are still patrolled. One way traffic heading south until Crescent Beach access ramp. Between Crescent Beach and Mantanzas access ramps it is two-way.
If you are looking for the recent drops over the past season, then focus your efforts around the access ramps (50 yards north and south). People are lazy. They like to drive on the beach, park, set-up the towels/tent, and play. They don't drive extended distances to find their own private section of beach for the day. They congregate around the access ramps. Also, during the season, that is where the life guard patrols are focused. Having only a couple of days, you might as well concentrate your effort with the likelihood of finding something.
You will have no problem detecting the beaches so long as you stay out of the National Park Service property (Matanzas access ramp heading south). And Anastasia State Park (Pope Road going North). Between those boundaries, you have 16 miles of beach to swing your coil.