Little Palm Island does have its own man made beaches. Very nice beaches in fact.

La Samanna is deteriorating. World class 10 years ago, now just upper third.
Cap Juluca on Anguilla is outstanding and very quiet.
Also check Grace Bay Club on Turks/Caicos. Very small/intimate, best beaches in the Caribbean. Easy to obtain accurate impressions from websites at gracebayclub.com and capjuluca.com.

James, we just returned from Hawaii and did almost all private villas. See my trip report on this forum (type maggi and click Hawaii in the search engine), for the details. I can recommend all the private homes we used, very romantic, very private for newlyweds.

Take a look at the J.W. Marriot Resort in Ilihani, Hawaii. My wife and I were there last December, it was quiet and beautiful.