St Barth Commuter (SBC) out of Grand Case is less expensive than Winair out of Juliana, if only for the departure fees. Winair has more flights, SBC is less expensive. Your choice.
Taxis are expensive, more so over the course of a day than a one-day rental car. On the other hand, parking in Gustavia is awful.
If by a nice lunch on St Jean you’re looking for something upscale then consider lunch at the Eden Rock hotel. If you’re looking for more of a party atmosphere then Nikki Beach. If you’re looking for high-end shopping, then Gustavia. My suggestion would be to fly over from Grand Case in the morning, rent a car (Gumbs or Top-Loc), take a drive around the island (counterclockwise or you may get stuck in Gustavia before you figure out the way out) and just follow the coast. It’s hard to get lost on an 8 sq mi island. Valet your rental at Eden Rock, melt the numbers on your credit card, and take an afternoon flight back to Grand Case.
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