Check out this link to a previous discussion on this subject:
You can fish off any dock that does not say "no fishing allowed". If you have a golf cart go all the way to the South end of the island and fish the channel there. You can wade and fish any where, but it depends on where you are staying and how much boat traffic there is. I have seen people catch fish wade off the beach in downtown area, but I would not recommend it!!!
As far as a fishing license is concerned - - yes it is required, no it is not and I don't know where to get one!!!
Have fun and tight lines!!!