A chic open-air hideaway. Premium restaurants. A half-acre lawn that boasts lawn bowling and a sunset bar. A 1,113-seat theater for Broadway-style shows. Ocean-view verandas.

Don't bother seeking out the roller coaster or the giant water slide on the Celebrity Equinox, the latest cruise ship to be based at Port Canaveral. There aren't any. The Equinox — and Celebrity in ...