In many places you'll get a better rate by paying in Eastern Caribbean
dollars rather than US dollars. The official exchange rate is about 2.7 EC per US dollar (2.6882 to be exact). Some vendors, especially in the touristy areas, will use a 2.5 EC/US rate, which costs you 7.4%. You get your EC dollars by using a debit card in the local ATMs, which are everywhere, as MarkJ noted.
If you want to use a credit card, be sure to get one that doesn't charge a currency exchange fee, typically 3%. We used a CapitalOne Visa card for that purpose. There are others.
The French islands use Euros, which can also be obtained from ATMs. St Martin
and St Barths will take US dollars. In Grand Case, St Martin
, many the (excellent) restaurants will give you 1:1 exchange for US$, a big savings!
Do a search for more on this topic--it's been discussed here frequently.