What kind of diners are you.
Foodies?
I would eat on the side of the island you are staying on for safety (no problems for us) and drinking.
While we enjoy all the island's restaurants from down and dirty to top of the line, my recommendations are as followed.

French side Le Pressoir in Grand Case (menu is different than traditional island menus) quality ingredients, husband / wife service team, beautiful atmosphere
and yes a bit more pricey but worth the splurge.
If food is your thing, the 7 course prix fix is a wonderful culinary adventure

On the Dutch side our favorites include Mario's Bistrot in Cupecoy, Jai's Contemporary Indian in Simpson Bay (although lacking atmosphere) and Emilios which is a beautiful restaurant

If food isn't your thing, there are hundreds of places to enjoy a meal