Excellent overview by View from the Wing on how to decrease the fees of foreign currency transactions while abroad. Here’s one that’s especially important and not necessarily intuitive:
Do not let merchants convert bills into your home currency. Always pay bills in the local currency. You do not want anyone to convert your bill to your own currency because they will charge you an unfavorable exchange rate to do so. You’re far better off with your bank’s rate than a local merchant’s rate, even if your card tacks on 3%. Besides, even after a merchant converts your bill to US dollars that credit card tacking on 3% is still going to add the 3% because it’s a charge originating outside the United States, regardless of the currency of the transaction.