I admit that I should have researched this part of our vacation prior
to our trip.
Uh, yeah. Cash exchange is one of the worst ways to get local currency. Not sure if the Post Offices will be open on the weekend. As Bets said, stow your US cash away in your moneybelt. Use your ATM card (NOT YOUR CREDIT CARD!!) at a bank owned ATM. Preferably AT the bank, and during business hours, in case the machine eats your card. Hopefully you notified your bank and CC companies that you would be using them in Europe (other wise they may freeze your account).
To avoid extra transaction fees, taking out one large sum (up to your daily limit) will be better than several small withdrawals. But the ATM will also have a limit on how much it will dispense per transaction. Once you've gotten your cash, head for the nearest bathroom (or your hotel room if it's close by). Put all the cash into your moneybelt except for the amount you will need for the day. Put your ATM card back in the moneybelt, too.
Best of luck on the rest of your trip.