One thing to keep in mind regarding "crowded" beaches (e.g. Seven Mile Beach), it's really only crowded where the cruise ship passengers go to day trip. Places like Royal Palms and Public Beach/Calico Jacks. The bigger hotels like the Ritz, Westin, Kimpton and Marriott (beach has eroded to a tiny sliver there) can be crowded as well; but while the all beaches are public in Cayman, the hotel's chattel is not, so other than restaurants/bar or water sports there's no reason to visit a hotel's beach. So if you stay in one of the many condo properties along the beach (they far outnumber the limited hotels), you'll be pretty much guaranteed to have a tranquil, uncrowded beach experience. Also the other major public sections like Governor's Beach and Cemetery Beach are alternative uncrowded options to explore.

With both Royal Palms and Calico Jacks slated to close, it will be interesting to see where all the cruise day-trippers migrate to.