GRAND CAYMAN—At a sunny beachside lunch earlier this month, concierge Bambi Grimotes was sketching an itinerary for a short stay at Palm Heights, a boutique hotel here in the Cayman Islands. Bambi—whom guests refer to mononymously, as they would Madonna—is the hotel’s master of ceremonies, whose job it is to hang out with vacationers, host monthly dinner parties and MC its increasingly packed Saturday karaoke night. “You would probably need some sort of massage,” he said, estimating that most guests need two days for their nervous systems to submit to the slowed-down pace of Palm Heights. “My goal is for you to feel rich. That’s how I feel.

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