Our Schwab card is chip and pin, no ATM fees, no foreign transaction fees, and can be used as debit card, especially important for automated ticket terminals (and we did so in Budapest last month). Our CapOne ATM card has no ATM fees, no foreign transaction fees, but is not a debit card - but can always be used to obtain necessary cash. They are both supported by bank accounts that we can move funds to electronically from our local bank account whenever we need to.
Our CapOne Mastercard has no foreign transaction fees.
I know there are other options, these are simply ours. You could get any one of these and then get her a card in her name, although the bank cards will require you to back and forth paperwork for her signature before they issue hers - unless you simply give her your card, since machines won't be checking for the name.
You say she is using her debit card for "cash advances". Do you mean she is using a credit card for cash from ATMs? This is going to do a lot more than just add foreign transaction fees, these all generate interest from the moment cash has been taken against them until it is all repaid, since it is credit transaction and not a withdrawal (while cash taken against a bank account by the ATM/debit card of that account is a withdrawal, not a cash advance). Living there she will be making lots of small purchases at places that do not accept credit cards, she needs a bank card. Even more so than a credit card, as all places take cash.