I would recommend the Eden Rock...it's a beautiful, unique hotel on a great beach. Guests from the past include Greta Garbo, Howard Hughes and Jimmy Buffett!! The rooms on the "rock promontory" are the best, but expect to pay top $ for the privilege. I stayed in a beach cottage, they're a bit small but everything is first class.
We have stayed at the Christopher for years. Much quieter location, but you must be willing and able to drive the roads. It often has specials on Luxury Links. I really prefer the Garden level rooms(less expensive) to the newly redone upper level which now has more inside room but no balcony .