St Maarten is another country (two other countries, actually... Netherlands Antilles and French West Indies), so you won't be able to use U.S. postage stamps from there.
<img src="http://www.dcltribute.com/images/postmark_st_maarten.jpg">
St Thomas is part of the U.S. Virgin Islands. Yes, you can use your U.S. postage stamps from there.
Castaway Cay is in the Bahamas. So the special Castaway Cay postage stamps are available only at the Castaway Cay Bahamas post office.
<img src="http://www.dcltribute.com/images/postmark_castaway_cay.jpg">
<table><tr><td align=right valign=top><b>St Maarten
<i>(Dutch Side)</i></td><td valign=top>US$0.65</td></tr>
<tr><td align=right valign=top><b>St Thomas</b></td><td>US$0.21</td></tr>
<tr><td align=right valign=top><b>Castaway Cay</b></td><td valign=top>US$0.55 for standard-sized cards
US$0.65 for oversized cards.</td></tr></table>
There are post offices conveniently located near each ship dock. In St Maarten, it is located in the complex of shops that are located in the first building you see upon setting foot on the dock.
In St Thomas, it is located in the Havensight Mall, no more than a 5-minute walk from the ship.
In Castaway Cay, you walk right by it before you even get to the tram.