It's hard to say which will be better in April. I prefer to set up camp at the south end. From north of the lighthouse to the south point there can be good structure and you also have the option of going around to the jetty, with good holes to be found between the point and jetty as well. If you are tent camping take a look at the wind forecast and try to use the dunes for protection if necessary. Don't set up out in the open.
You'll want to at least come over with fresh shrimp. If you can find or net fresh jumping mullet that would be a bonus. Try http://drumwagon.com/fishrep/. That forum will have more folks familiar with the island.