Getting to the Island
I will start off with saying that you must have a boat or watercraft to make it to the island. The tour boats that go to the island are not dropping people off and leaving them there for camping.
Directions on how to get to the Anclote River Park are as follows. Refer to the map below if you need. Basically, you need to take US 19 to ALT US 19. Then, turn off onto Anclote Blvd. and follow it to the Anclote River Park. At this park are boat ramps. Below this map is a close-up of the Anclote area. Also, you can see the Anclote Keys partially on the western part of the map.


On this map, it shows a close-up of the Anclote River Park. I would also like to identify the Anclote Gulf Park. I am not sure if there are boat ramps there, but I believe you can actually see Anclote Key from there. The island is not visible from the Anclote River Park.
Once you are in the water, go out of the Anclote River and into the waterway. Head to the island and go around the southern tip to get to the lighthouse area. There are pit toilets and picnic tables by the lighthouse and also on the northern tip of the island.
Also below is an aerial photograph from Mapquest.com of the Anclote Keys. It was taken at night time, so it did not come out really well.
