From GoToCayman.com - the Wiki for Cayman
The Cayman Islands have their own currency - the Cayman Islands Dollar (CI$). However, the US$ is accepted everywhere at the standard exchange rate of US$1 = CI$0.80. The official bank rate (if you want to bother queuing up to change your money) is US$1 = CI$0.82 - you will only be able to do this when on the island as most banks in the rest of the world won't hold Cayman currency. Some shops also offer this rate (notably Kirkconnell's supermarket). You will usually be given your change in CI$.
I once tried to change GB Sterling into CI$ on the island; the bank first of all converted my Pounds into US$ at the current market rate, and then from US$ to CI$ and then charged me two lots of commission! Moral of the story is to bring US$ only!
The main ATM networks have machines on the island - as most of the banks are in the George Town/Seven Mile Beach area, this is where the majority of machines are located. You may also find machines outside some of the bigger supermarkets and at some petrol/gas stations.