As has been brought up, the best place to get your Euros is at an ATM. They are everywhere and will give you the best exchange rate.
The daily limit might be a problem for you because you need money right away for your lodging. Typical daily limits on ATM cards are $500 (not the same as 500 Euros) and refresh daily (normally at around midnight at home). Daily limits are designed to protect you if your bank card is lost or stolen so your entire account won't be cleared before you call the bank.
A couple ways to get around the daily limits:
First, ask your bank to increase your daily limit when you advise them you will be traveling to Europe. Some banks will increase your limit at your request, most won't.
Second, use more than one account. When I travel, I bring an ATM card for my account and my wife brings a card for her account effectively doubling our daily limit. Both accounts are at the same bank and, since we're both signers on each other's accounts, we can transfer funds if one card is lost or stolen. Many accounts are free, you could conceivably open extra accounts just to have an additional debit cards and daily limits.
Third, order Euros ahead of time so you have the currency you need. Any commercial bank can get Euros for you but you usually have to give them a few days notice (sometimes they have a small amount on hand in the branch).