Philosophically, the amount of money one spends on food, drink, and incidentals can give rise to a false economy, one that tends to elevate thrift over experience.
As an example, I ate dinner in a Brasserie in Paris some years ago on the Left Bank. It was a famous place, and I expected the experience to be really good. Because the prices seemed high, however, and because I wanted to stick to a budget, I ordered by price, rather than by which dish I actually wanted. The result was a lackluster dinner, and a "meh" experience overall.
I returned to the same Brasserie on a subsequent trip, and this time, I concentrated on getting what I wanted, rather than what was cheaper. This time, the meal was memorable, and the experience was wonderful. The difference in price between the two dining experiences was less than $15, and I have never regretted that expenditure.
Similarly, a panini from a small salumeria in Rome may be all I want, or I may decide that a splurge is in order. Set your budget, but don't panic when you actually spend more for a memorable meal. Some years ago I heard about a small trattoria in the Jewish Quarter of Rome, Sora Margherita. It was an incredible experience, although the price seemed high--about 30 euro each for lunch. Today, the prices have shot through the roof. Would the experience be as memorable? Probably not.
I love making my own breakfast in an apartment. Standing at a bar for a coffee in the morning just isn't my preference. I will, however, use a coffee break as a way to get access to a restroom on site. I don't curtail my gelato cravings, nor do I refrain from sampling street food when the urge arises.
Just remember that food and eating (and drinking) are part of the experience. Would I go to a Michelin starred restaurant in Venice or Rome? Probably not, because that's not how I eat at home. Would I balk at spending 15 euro for a bowl of cacio e pepe at a renowned local trattoria in Trastevere? Absolutely not.
Do some research into "the best restaurants" in each city. Often these guides can single out the hidden gems where your Italian adventure can be made even better.
A word on drinking. Alcohol is a personal choice, but in my world a glass of wine or two at dinner makes the meal complete. I also like a cocktail from time to time. Little markets stock all kinds of booze, and rather than haunting the nightclubs or bars for a post dinner drink, I buy my own spirits, beer, or wine in those markets for consumption in my apartment.
Have a wonderful trip!