A1A is the actually the road the resort is located on. There are 'sidewalks' that run along the length of the road, for miles. They are offset from the roadway itself by a good distance. I'm thinking 10 feet or more.
The sidewalks do not run on both sides of the road. From the resort, just walk out the front. You'll need to cross the street. Either watch for traffic closely before crossing, OR take the tunnel under the street, then double back to the sidewalk.
As to the jungle trail, if that's the trail on the VB property across the street, it's no good for jogging, only hiking. There's a park not too far away that also has some trails going back into the woods/brush, but again those would only be good for hiking, not jogging. (They're really paths, not trails).
As mentioned, the beach sand is way too soft for jogging. If you got right to the water's edge at lower tides, it's more firm, but would still be more of a workout than running on pavement or dirt)