I too would recommend the French side beaches for the kind of eateries you're looking for. As said by others above, Baie Rouge, Baie Nettle, Cupecoy and Friars Bay all have that kind of thing; I like that too so I can vouch from experience.
Enjoying the beach or the sunset with a plate of jerk chicken, ribs, slaw and rice with a cold Carib is livin' the high life, I'll tell ya !
There are many other beaches which do not have food/drink services but are stunning for atmosphere/natural beauty/privacy,so pick up cooked specialities and drinks from Marigot or the lolos in Grand Case before you go.
You will also certainly need a car as has also been mentioned before, to easily get to some of these places, so plan for that. Its not difficult to drive around (the island is small) though traffic can be frustrating sometimes. Maps of where everything is located are available free at the airport (you can't miss them).
GCBC is a good hotel, but there are many others. Depending on how much priority you put into your accommodations, there are other mid-level French chain hotels on the French side close to some of the beaches mentioned, such as the Mercure hotel and Le Flamboyant next door to it. Another decent hotel right on the edge of Marigot and within walking distance to some nice restaurants in Marigot Marina for evening dining is the Beach Plaza hotel, which caters mainly to a business clientele. Look them up; English and French spoken at all. A full b'fast usually included in most plans.
Good luck and enjoy.