Do I need to carry any cash?

Maybe some coins for restrooms.

And in Turkey you will need cash in some smaller towns for vendors, markets, and some restaurants may not take credit cards or electronic payments. There may also be the occasional minimum purchase required to use a credit card.

Sometimes you get a discount for using cash. Once or twice the credit card readers were out of service and cash only was required.
For the most part Credit cards are accepted everywhere now.

As wonderful as swipe and pay is I have personally encountered; 1) A cab whose internet connection for any cc failed; 2) Greek shops where cash particularly coins gets a discount ; 3) Tour guides in several cities who required cash beyond tips (and we were informed when we booked that the booking agency billed for the majority of the tour but the remainder needed to be paid directly to the guide in cash (the total was as advertised so we were not overcharged, but....). My initial extra 100 euros has been back and forth several times before it was all used... but it was nice to have. And a small amount like that didn't create significantly large exchange fees.

hey hey craigmwatts1
as others have answered, i agree with them. i always have about 50E and do have coins which came in handy. many places like cash and many give discounts, some places you have to spend so much to use debit/credit card, other say CC machine "out of order".
they get charged and send that charge to you, just like in the US. some agree some don't.
i do not want to be roaming around for an ATM machine. it's just convienient to me. if need money from ATM i always choose an odd # 85E or 95E to get smaller bills and not a 100E bill.
it's your vacation and your decision. i always seem to have a small amount coming back to USA, keep in passport to use next trip to euro country. make sure an ATM and not euronet machine that charges "BIG BUCKS!" in fees.
have a great time, enjoy and have a shot of ouzo :)"
aloha

Some cash for tips etc, mostly card, but take note that American Express is not widely accepted, Visa & Mastercard are the ones accepted everywhere. ATMs dispense 50s & 20s so choose an amount like 80€ or 180€. Do not use Euronet, the main banks to use are Piraeus bank, Alpha Bank, National Bank of Greece (NBG) or Eurobank, if you’re going to Crete (& there’s some branches in Athens & elsewhere) Pancreta & Bank of Chania are also Greek banks.
When withdrawing do not accept the conversion offered, you may be asked again if you’re sure, stick to your guns & go ahead with no conversion, the difference in rate can be quite large.
I live here & as a guide we probably spend a total of about 80€ month in cash between us, everything else is with a card. If paying by cash ask for & make sure you get a receipt.

Most of the responses appear to be from the standpoint of traveling in Greece, where I have not been for decades.

I can tell you that not having any Turkish lira may well be a problem. I spent a month in Turkey in 2023, split between Istanbul (mostly) and Bursa. I encountered quite a few restaurants that didn't accept credit cards. One that did take cards really leaned on me at the end of the meal to pay cash. I'm not much of a shopper, but I think you could run into the same thing at little shops.

You shouldn't drink the tap water in Turkey, so (unless your hotel supplies bottled water) you will be stopping frequently in small shops to buy liters of water. They look like they're run on a shoestring, with little profit margin. Are you going to want to pull out a credit card to pay for a bottle of water that costs less than $1 US? I'm not comfortable doing that even if the shop doesn't have a minimum-purchase requirement for using a credit card.

Mosques without entry fees, like Christian churches, often have a donation box into which I like to drop coins. I don't recall seeing credit-card readers in that situation, though they do often show up (though not always) in other European countries.

Edited to add: Mosques usually have toilets in a separate building. There is generally a small fee. I can't imagine trying to pay it with a credit card.

Greece now makes it mandatory for all business to accept credit cards so shouldn't be a problem anywhere.

However, I always have some Euros on hand for small purchases, tips, and in small out of the way areas.

Some business will give you a discount if you pay in cash like accommodations or car rentals but there is some controversy regarding that as cash doesn't leave a paper trail and business can avoid paying taxes.

I've paid cash for accommodations and car rentals so do what's best for you.

"Greece now makes it mandatory for all business to accept credit cards so shouldn't be a problem anywhere." ...unless one of the not infrequent power cuts renders the POS terminals useless

Keep in mind, Greece uses the Euro. So do about 75% of EU member nations. Any Euros not used in Greece can be used on a subsequent trip to much of the EU.