I'm wondering how much cash (euros) we need to bring with us to Santorini for a week?
I have heard that the local restuarants do not accept credit cards so figure we'll be needing some cash. Are there ATMS on the island--in Oia and Fira? if not, how much cash will we need per day?

Yes, there are quite a few ATMs in Fira. I also saw one in Perissa (beach), but I wasn't looking for one in Oia.

Credits cards are accepted, especially for shopping!

ATMs are popping up all over on the Greek islands these days. A small island I go to every year had no ATMs four years ago. Then one appeared, and last Spring there were three. I usually bring just enough cash in Euros to get me to Piraeus, buy a ferry ticket, and pay for a meal or two enroute to the island.

It's always a good idea to have a backup source of funds, eg traveler's cheques, in case something happens to your debit card.

How accepted are travelers checks in Greek Islands? So, most places won't take a credit card? Where's the best exchange spot to get euros?

Traveler's cheques are a pain. Because of the limited hours of operation of banks, you end up cashing them in at travel agent's and they charge a commission. ATM's are a much better option. Carry an extra withdrawal card for a back up plus you can always get a cash advance on a credit card if something goes wrong. There are ATM's in Fira. If travelling to a small island and you are not sure if they have an ATM just take out extra cash.

The only island in Greece I can imagine not having an ATM, would be a tiny one, with no buildings on it at all. ATMS are everywhere in Greece. And I don't recall hitting more than one or possibly two restaurants in an entire month of the islands that didn't take credit cards.

There are several ATMs in Oia. And most everywhere takes credit cards.