Another Euros question

Most take credit cards, but for the occasional tip, toilet in a station, or a quick coffee or gelato, or a rare cafe that doesn’t take cards, having some cash is a good idea. We would generally have €200 on hand for possible needs and use any fund remaining for needs (meals, souvenirs) on the last day.

We too like to have about 200 euros in hand while in Italy for all of the incidental expenses Laurel mentions.
The best way to get the money is with your debit card at a bank operated ATM after arrival ... although I've generally found that requesting an odd amount (ie 190 rather that 200) ensures that I won't get stuck with four 50 euro notes which can be difficult to break for minor purchases.
All that said, if you'd prefer to have the money in hand upon arrival you can head over to any AAA office and purchase currency from them. There will be a slight premium markup applied so you won't get a great exchange rate but for a minimal amout like 200 euros is doesn't amount to much. BTW, they run the transaction thru Wells Fargo, so if you have an account with them you can purchase your foreign currency directly from them.

Are there some restaurants, shops, tourist sights (especially in the in the Dolomites, Cinque Terre and hilltowns) that don't take credit cards?

Even the tiniest shops take credit cards. In my last three trips to Italy, and Europe in general, I’ve only spent cash thrice for a total of less than €100. I mean it’s good to have some cash on hand but no need to be carrying around large amounts of cash like in the past. In Europe all CC payments in shops and restaurants are Tap and go, no need to insert or swipe. Use bancomats (ATM) to get cash, official ones at banks and not freestanding ones. No need to use money changers as their fees are usually astronomical.

Someone else mentioned tips. Tipping in Italy isn’t a part of the culture and some areas see it as an insult even. All eventuale are included in prices. Good luck and happy travels!

Italian merchants must accept credit/debit cards mandatorily by law regardless of amount since 2023. The only exceptions might be the notoriously dishonest tax dodging taxi drivers who will tell you their POS machine is temporarily not working therefore they can only accept cash. Italians don’t leave tips, but if you are one of the Americans who can’t help themselves and must leave a tip, you will need cash because you can’t add a tip to the credit card bill. You might also consider it more convenient to pay cash for small purchases, like an espresso (just over one euro). Of course if they offer a substantial discount for cash, then take it. Remember however that credit cards give the best exchange rate, therefore if the cash discount is less than 5% it is not worth it.Use the card in that case.

There are still hotels in Italy that require you to pay the city tax in cash. Probably not 4-star and 5-star hotels, I would guess, but definitely some 3-star places.

When I took the Best of Italy tour in 2022 I was doing a trial to see how often I could use Apple Pay. I literally used it everywhere including the 3E gelato I got in Venice. I did need coins when I used the public toilette in Verona (lunch stop between Dolomites and Venice) but that was the only place.

The only times I needed cash were to pay a bar bill at the end of our stay at Hotel Pasquale in Cinque Terre (OMG get a limoncello spritz if you are staying here!) and at the Altarocca Resort outside Orvieto. We were told this ahead of time so I had some cash.

I used to go with the 200E amount but since Covid so many people accept contactless payments that it's easier to do that. I just keep the cash as seed money for my next trip.

I'm also a solo traveler so I had a couple of times on my last non-RS tour where I split a meal bill with another solo traveler. Sometimes the restaurants (France) would divide it up, sometimes they would not so I did have to use cash on those occasions.

If you don't currently use ApplePay or GooglePay, I encourage you to do this now. Practice at your local grocery store, pharmacy, restaurants until it feels natural to you. This is the norm in the places I've traveled in Europe.