I have never had a problem getting cash at an ATM in an airport. There's usually a machine in the baggage collection area, always at least one after customs. Worst case, change a few dollars (I assume you'll have some with you, unless you plan to arrive at the airport penniless) at an exchange if the machines aren't working. There's always a manned currency exchange. You'll pay more that at an ATM but probably a lot less than buying in the U.S.
Both countries have ATMs everywhere. You'll be able to get local currency at the train station when you arrive in the second country, probably .
I'll echo others - do some research now to get a credit card and an ATM card with the lowest rates possible. Do not use a credit card to withdraw cash.
To the general discussion about limiting percentages charged to merchants by credit card companies, I wonder how much the merchants are paying. When I first went to Italy 7 years ago, most hotels gave me a 5-10% discount for paying cash. In recent years, the response has been "cash or card, we don't care, same price either way." The only time I've been offered any discount is by booking via email or phone, since booking agents take big fees. Even hotels that have booking on their own websites are paying fees for that service.