You'll almost certainly be staying in likeable, laid-back
Oranjestad
if you stop overnight on Statia. If you're just here on a day trip, it'll take you at least a couple of hours to have a good look around, and there are several places where you can get a splendid lunch.
While the town is rather sprawling, you'll want to confine your exploring to the main points of interest in the centre.
Upper Town
is where most of the (leisurely) action is, and makes for a pleasant place to wander and visit the island's museum and main colonial buildings. Linked by a footpath to Upper Town,
Lower Town
is the area of the old port, now home to the best beach locally and further ruins of the island's once-great past.