Is there still a limit on daily Euro ATM withdrawals in Greece? Does this vary from place to place? Is it posible to go into a bank and get more than the ATM limit?
The limit was only for Greeks using ATM/Debit cards issued by Greek banks. If there still is any limit imposed by the government it is nationwide.
No, a bank cannot and will not give you money on a Debit card if you go inside. You might be able to get a cash advance on a Credit card inside the bank, but then you will be hit with the associated high interest rates and fees and transactions not done through an ATM do not have the guarantee of the lowest possible exchange rate.
Greek banks do not place a limit on ATM withdrawls for tourists. The limit is for Greeks. Your own bank however will place a daily limit on what you can take out. Let them know you will be in Greece and using ATM.
We normally take out sufficient cash to last a few days and usually get 300 euros but once were able to get 500. Acceptance of credit cards is becoming more common in Greece now so reliance on cash isn't quite as important as it used to be.
The strict small daily withdrawal limits only applied to Greek residents. Foreigners can always withdraw the daily limit set by their home bank. Individual ATMs can have a single transaction limit, sometimes 300 or 500 euros, in which case you can still make multiple transactions at different machines or times to reach your personal daily limit.