JBSTL--Since you're staying at Royal Palm, you may want to try out Roxxy, if it's open. I don't know whether they are closed for vacation now or not. It's literally next door to RP. It's very high end. I haven't been there myself, but you can always walk over for Happy Hour and see whether you like the menu and the ambiance or not. For French cuisine, I would echo Jazzgal's recommendation of Le Moulin Fou. For a toes in the sand experience, you may want to check out either Karakter or Mary's Boon. Neither is high end food, but it's a lovely stretch of beach there.

I will be interested to hear when you arrive if the restaurant at Royal Palm is open or not. IF it's open and you go there, don't expect much. Historically that restaurant has been VERY bad.