If you're renting a car why not stop other than P'Burg for lunch. Suggestions:

Grand Case Beach Club's Sunset Cafe has full meals & sandwiches overlooking island of Anguilla, Creole Rock and the beach.

Calmos Cafe in GC you can eat at tables in the sand on the beach.

Or one of many seaside restaurants. Get a table overlooking water if you don't want to eat open air.

If you want to beach it try Dreams in Nettle Bay. Free chairs with plush cushions if you eat and/or drink. Or eat at a table in the semi open air restaurant. Gourmet food, pizza, sushi.

For an exciting ride go to Ansel Marcel up and down a winding road to beachfront. You can dine on the beach or in the restaurant.

Yacht Club near bridge Simpson Bay watch the boats enter or leave or just moored. Good food great bloody Mary.

Or one of the many places out of P'Burg then return for a cocktail in P'Burg or dessert before leaving for the ship. I agree Antoine's is the best choice in town.

We gave this advise to friends who came in on a cruise and they opted for a stop at Sunset Cafe Grand Case but ended up staying there on the beach. I think they should have seen the rest of the island.