Going from Downtown Gables, take Biltmore Way South-West to Segovia; go south/left. Follow that until Riviera Drive. Take Riviera south/left all the way to LeJeune (it sort of ends there). Take LeJeune South to cross small bridge into Coco Plum Circle. Stick to the right, and go around the circle until you get to Old Cutler Road. Take old Cutler South/right (using sidewalk) all the way to Hammock Park. In Hammock Park, take the bike path on the left, all the way to the beach.
I reccomend taking time to enjoy the view of the bay and the city. Maybe even trying a swimm. The snack bar closes early, so if you plan to stay at the beach late, bring a snack for fuel on the way back. There are no restaurants along this route.