What is your reason for needing an "offshore" account?
I have a checking account with Wachovia here in the US. No annual fees. No minimum balance. I lived in the Caribbean for 2 years and this was the only bank account I had. I have used my ATM/ VISA Check Card throughout much of the Caribbean as well as in Europe without ever having a problem. The only problem is that you get charged a bank fee of $1.50 for using at a bank other than wachovia.