This is my favorite hotel/spa in the world, hands-down, and an easy trip from New York when looking for a short getaway. The thing that distinguishes this place for me from everywhere else is that the whole place smells like a spa and the customer service is unparalleled.
I've stayed at other hotels in Miami and a night or two in one them might be nice for the South Beach vibe and partying, but if you are looking to get away to relax and for a little quiet and privacy, the Mandarin Oriental Miami with its own private man-made island, amazing food at all of their restaurants, and the luxurious spa is all you really need and a great way to cap off one's trip. The thing that makes this hotel extra special unlike the other Mandarin Orientals (like the one here in New York) is that the whole hotel smells like a spa from the lobby to the hallways to the rooms. It is utterly relaxing.
The service here is unparalleled from entry (I was greeted with a complimentary service) to exit (was personally walked out to my cab to the airport by the front desk). Everyone is exceedingly polite in that Asian-style way and as others have reiterated, they make you feel so special that by the time you leave you are convinced that you are indeed special. ;P
The spa here is also my personal favorite spa. The waiting lounge area has snacks and has live soothing running water going, they play a gong before the massage (to clear the air), they customize your massage for you, and you have to try the amazing thunderstorm shower that pelts water at you from all angles while making thunderstorm noises after your treatment. I remember coming back up to my room and passing out on my bed and thinking I felt so good I could just go now and be at peace. I actually made sure to buy their spa products before I left so I could take a bit of the experience back home with me.