Daily food budget

You could look at some menus in the places you’ll be going and get an idea of what meals would cost at the kinds of places that interest you. The costs could vary greatly based on the places you choose. You can then tell them you’ll pay up to x€/day for food. If they want to spend more, they’re adults. They can put in their own money.

I go to Florence (the city where I was born and raised) at least once a year (pandemics permitting). Although prices may vary from restaurant to restaurant, on average my wife and I never spent more than €35 per person per meal, for eating at a sit down restaurant (and if you see me in person I’m sure you will not think I eat little). There might be restaurants a bit above that or a bit below that, but at the end of each trip that was our average range for sit down restaurants (and I am a professional accountant so I love to keep track of that stuff). Obviously you will spend less if you eat a sandwich at a deli, but those are the average prices for a sit down restaurant, and they include wine (lots of it since I drink a lot too). Venice is slightly more expensive but not significantly so. Alcohol is generally significantly cheaper than in the US. Soda is expensive, so don’t make the mistake to order coke instead of wine (and that includes your kids since drinking age is 18 and nobody even checks if you are a minor). In the SF Bay Area we spend almost twice the amount of food we spend in Florence (for either restaurants or groceries at a the store).
Earlier this month I posted several reasonably priced authentic restaurants in Florence where you can stay even below the range price I gave above.
https://community.ricksteves.com/travel-forum/italy/top-restaurants-in-florence

Breakfast at the Airbnb should/could be provisions you bring in for the family. At hotels, it is most likely included so no need to allocate a lot of Euros there.

Lunch can be €10-20 depending on amount consumed. Sandwiches in bars (aka cafes to us) are usually good and inexpensive but you/they might have to eat them standing up. I used to pick up a great sandwich near my office for €5-7. You usually pay extra to sit down but it can be worth it to take the load off and rest for 30 minutes. The buffet places (called a Tavola Calda) are good and depending on the neighborhood, often the haunt of the business people who know a bargain. Not all-you-can-eat but ample, simple food, well-prepared. Pizza is a bargain, of course.

For dinner I would allocate €30 per person and if you run under one night tack it on to another night for a special dinner. Maybe at your Airbnb one night the chef can cook! Wine is inexpensive in the grocery store and you can get a decent bottle for €10-12 or even less depending on your taste.

In over 15 trips to italy, our average daily food cost has been 60-75 $ p/p a day.

Staying in an apartment has not noticeably dropped food costs because there are so many tasty items to bring back to lodging to sample

Great suggestions and…

—- if you order wine in a restaurant get the house wine.
—- if you eat breakfast out, order coffee and pastry standing up. Same for a mid-morning coffee.
—- stock up on a few basics (eggs, milk, cheese, and a bottle of local wine, of course).
—- consider having your big meal of the day at about 1 pm then have gelato, apertivo and/or a picnic at dinner time.
— find places that serve nice snacks with your evening aperol spritz. People watch while you drink and enjoy your snack.

Oh… as Rick suggests, find small, family owned places that are not on the main piazza. You’ll have a better meal and experience … for a reasonable price.

Enjoy!

Second the suggestion to look at menus of places that sound interesting. Your tastes may be way more than mine, or vice versa, so context matters.

However, my wife and I eat very well in Italy on a 100 euro a day for the two of us. That is usually coffee and something small in the morning, a decent lunch, but maybe a sandwich or pizza, and then a dinner (or we may eat this mid day and snack at night) with an antipasti, a primi or secondi, some side vegetable, wine, and either dessert, or go someplace for gelato, sometimes an after-dinner drink.

If your interests are seafood or steak, then that price goes up, but you could also eat well for less.

As for drinks, it can vary greatly by location, but generally a house wine is cheap, mere euros for a carafe, bottles can run similar to the US, but better quality for the money, 20-30 euro will buy you a very nice bottle. (Wine for the apartment, from a store, is dirt cheap for the quality though) Beer is cheap, but not very good, unless you buy craft beers, which are OK there (rarely great), but similar in price to the US (5 euro?). Cocktails vary the most, they can run similar to the US, though you can find an Aperol Spritz for 5 euro in some places as a tease. Soft drinks will run you more than wine.

Bottom line, if 50 euro each is good for you, and they will pick up the difference, then that is a good target budget.

Italy is different- our recent experience was 3€ each to sit down, 3€ for water ( enough for two people), then house wine half-liter for 7€. Of course, we didn't tip 15-20%, just rounded up the bill, or left 4€ for the two of us, and the wait staff seemed very happy with that, as when we returned to some of the same places, they brought us complimentary dessert.
Safe travels!