It couldn't hurt to bring a couple hundred Euros with you. But I believe that ATMs in Greece are now working normally. From what I've read, you may find an occasional ATM out of cash, but that can happen anywhere. To reassure yourself, if you're still worried, you could email a couple of your hotels (in Athens and islands) and ask what the ATM situation currently is. Be aware that many restaurants (and some small hotels) do not accept credit cards so you will need plenty of cash.
It would be very helpful if you would report back and let other travelers know about the ATM situation, once you get there (or soon after your return).
In case you're tempted by the prepaid American Express card mentioned above, there was a long discussion of it within the last week and the consensus is that it's a bad idea. Here's a link to that thread.
I do what Janet does ... I have a separate checking account with ATM cards that we use only for travel. Ours is through USAA Federal Savings Bank. Anyone can open an account there. It's totally free ... no monthly charges. No minimum deposit. No ATM fees. No foreign transaction fees. I think there's a small foreign currency conversion fee. We have this account linked to our everyday checking account, so we can automatically transfer money back and forth as needed. Easy and secure. We have one account, but they gave me and my husband each a separate account number, so if we lose one card we can still use the other. And like Janet, we do carry a back-up ATM card as well, as well as a couple of credit cards.
Enjoy your trip!