St.Eustatius, commonly called Statia, is one of the islands of the Dutch Caribbean. The island is basically a dormant volcano, shaped like a saddle. The airport is situated in the extinct crater, flanked by two hills. You probably won't visit the island just to watch airplanes, but nevertheless, the airport provides some interesting views. The only airline currently serving the island is Winair from St.Maarten.
F.D. Roosevelt features a single 06/24 runway. The terminal is located on the south side of the runway. The north eastern tradewind causes aircraft to use runway 06 most of the time.
The airport is situated just north east of the capital Oranjestad. Considering the size of the island, you will not have any trouble finding it, in the unlikley event you will arrive by boat.
Around the Airport
The terminal area is very open and provides good views of aircraft parked on the field's small apron.
Since runway 06 is mostly in use, your best bet to witness some flying activity is west of the terminal. From the terminal, head to Oranjestad by keeping the airport fence on your right. Just after the intersection, you will have ample room to find a spot of your liking.
St.Eustatius has a relatively large number of old forts; one of these, Fort Amsterdam, is located near the 24 threshold. If runway 24 is in use, aircraft approach over the sea, providing a great photo opportunity.