Half Moon Cay is an island near the Bahamas, I think, that is used as a "private" island for Holland America ships.
CCL owns Carnival and Holland.
The island is gorgeous...beautiful crescent shaped beach, chairs (some with umberellas), snorkeling, parasailing, bannana boat rides, floating mats, a little church, pavillions, nice restrooms, one tiny shop and some stalls for local crafts and hair braiding.
Holland America prepares and serves a BB-Q lunch under the pavillions.
I've been to Labadee, and to me, Half Moon is far better.