ATM owners don't charge fees to withdraw cash in Portugal, regardless of your home bank or card issuer. (Of course any fees charged by your home bank / card issuer, e.g. for foreign transactions, are separate and still apply.)
Does this include ATMs on the Azores? Do the owners of ATMs on the Azores charge visitors fees to withdraw cash?
My card was issued in the USA, are there special fees for non-Portuguese/European cards?