DR has a floating rate although the government does their best to keep is reasonably consistent so not to shock the economy. Just google "dr pesos to usd" and they will give you a nice graph. 58.45 pesos to 1 $ by that source. Click on 5Y to see this graph:
That big drop was a killer for poor Dominicans importing everything was more expensive and the price of chicken was changing almost daily. However, with the flow of tourists, there were definite shocks to the economy. Historically, the rate has been about 7% which is why things like real estate is often sold in dollars.
Other counties will peg the rate to a hard currency like the dollar and their are French/Dutch caribbean islands that run on Euros. Panama is 1:1 with the dollar, and which makes it easy to spend your americanos where you want.