Here's a link with a map of the area for both Sullivan's Island and Morris Island. http://www.bansemer.com/nc-lighthouses/morris_island_lighthouse.htm
You just take 171 to the end in folly Beach, turn left and go to the end of the road.
Just before the barrier (about 200 yards) is a little parking area. You then walk about 1/4 mile past the old Coast Guard station and down to the beach.
You are right next to Morris Island and you can see Sullivan's Island across the Harbor. It's more difficult to see Morris Island from Sullivan's Island.
You can see both of them on the boat trip out to Ft. Sumter.