Most places have stuff priced in US dollars.
It's pretty common to get your change in Peso's. They'll often "accidentally" give you the change back incorrectly. (meaning they steal from you.)
I've had this happen numerous times. Especially when a resturant bill is in Peso's and you pay them in USD. Have someone in your party that has a purse keep a cheap pocket calculator in it. Pull it out and you can do the conversion quickly. It's amazing that a couple times when we pulled out the calculator at dinner (at places that were in Peso's) that they often came back to the table and took the check back and said they made a mistake and brought the wrong change back with this check and to let them fix it quickly. (meaning they realized they were about to get 'caught' in the act of trying to cheat you.)
you can also ask them what "exchange rate" they offer at the store/restaurant. You can expect it to not be as good as it is at banks, etc, as they are making a little money on the exchange.
Paying with your credit card offers a pretty decent exchange rate since it's done by the bank card company. It will always be charged in Peso's though intead of dollars most of the time. So if you're at a store and you agree on a price in US dollars and then they charge you in peso's, make sure they computed your charge at an "exceptable rate" that is comparable in pesos. they might try to rip you off here also. Right now the USD equals about 11 pesos.
BTW... I've yet to visit a Caribbean location that does not accept the US dollar. It's even pretty wide spread in Cuba.
oh... one more thing. No matter where you are in the caribbean, you typically get coin change in the local currency even if they give your paper money back in USD. While this might cost you a few cents, it's under a buck and it's just pretty widely accepted and not haggled over. Just think of this as 'neat' to get the local coins and then give them to kids of friends back home as small gifts. Kids just love getting coins from other places.