score:3
I come from nearby (Grosseto). Cortona is a medium sized town, so there will be plenty of cash machines accepting either visa or mastercard (with credit your are safer than debit cards). In the last years many places have started accepting contactless for small transactions, but surely most bar won't accept chip and pin for drinks. Most restaurants will likely accept chip and pin, likewise the supermarket. That said, in small centres like this, what most people still do is to take money (50 or 100 euros each time) from the cash machine and use that for everyday purchases. Also if you are from abroad, you will likely pay charges every time you pay or withdrawal, so using the card as little as possible is going to be cheaper.
Upvote:3
In most places, you should be able to pay with your credit card and/or debit card.
Conventional wisdom says that you should also have some cash on yourself; mostly for small purchases (like taxis, coffee, gelato, ... ).
If possible get some euros before leaving to Italy, something like 200euros; after that, if needed use ATMs to get more cash.
Also, don't forget to notify your bank and credit card company that you will be traveling to Italy (with dates) so that your cards don't get blocked by mistake.