If you're traveling in less than a week, you probably don't have time to open a new account with a new bank and get the cards before traveling, but you could try (Schwab is my favorite for both ATM and credit accounts, with no fees, unlimited ATM fee rebates, and 2% cash back on the credit card). See the wiki to see how Citi stacks up against other options. It's definitely not ideal, but it's still probably better than trying to exchange cash, so go with it if it's your only choice.

There are no published exchange rates. They change constantly (from moment to moment) along with the foreign currency markets and there is no way of knowing what rate you will get until the withdrawal/charge hits your account. When you withdraw 100 euros from an ATM or make a 100 euro point-of-sale purchase on your credit/debit card, your account will be hit for the equivalent amount in dollars using whatever exchange rate the bank uses + any fee the bank tacks on.