Thanks everyone for suggestions! We are thinking to go to Pinel island tomorrow, and will try Anse beach on Thursday.
The other beaches, not sure if I can endure more traffic here. It just took us more then an hour to get back to our hotel - Orient Beach Hotel from Mullet beach.. I am all for exploring other places, but I don't want to deal with crazy traffic. I have enough of it in NY.
I was reading more about Oriental beach, and it appears that more often than not there is a strong wind and rough ocean. Yes, the idea was to explore different beaches, but I did not envision not to be able to spend any time at the "base" beach and definitely did not expect crazy traffic there.
I will provide more details about my trip as it goes, but at least for now, we have our most enjoyable part of the trip coming up -the dinner! We booked Ocean 82 restaurant based on glowing reviews.