I love St. Barths, but mainly because I can anchor for free in Anse Colombier.

The walk to/from Anse Colombier beach to the main road is 20-30 minutes along a wonderfully scenic path. This is, by far, the best beach on St. Barths
Second best beach is Anse a Flamands
Shell Beach, just 10 minutes from downtown Gustavia, is always worth a visit.
My favorite, and least expensive, alternative to Haute Cuisine in St. Barths is "Le Select" (a.k.a. Cheeseburger in Paradise) right in the middle of Gustavia.
The roundabout above the airport offers great pictures and views of aircraft landing.