Luxury, Non-Zoo-y Resorts in Bahamas, Grand Cayman

My wife and I have unexpectedly come across some free time in April, and are looking to book a last minute vacation to the Caribbean.

Given the flights, it looks like the best islands for us are going to be the Bahamas or Grand Cayman.

Given the above, any recommendations for resorts? We’re looking for something upscale, luxury-feeling, and relatively quiet (i.e., not a total zoo), but also very close to lots of dining options. Budget is between $400-700 a night for the room. So far, the leading contender from my online research is the SLS Baha Mar–but I haven’t ever been there (or to either of these islands), so this is really just based on TripAdvisor score.

Given these parameters, what would you all recommend? Also open to other islands, if there’s a can’t miss place that we’re not thinking of!