If you are staying in a hotel, breakfast is usually included. I look at booking.com for photos and reviews, if there's a good breakfast there is likely to be a photo or comment about it. If you are staying in an apartment, I would just get a cornetto or other pastry and drink at a stand-up bar to start your day. Many cities have a "tavola calda" or more, eat-in places that are cafeteria style. There are lots of places to take out food as well, if you have an apartment. Be careful about picnicking around public monuments, it's illegal and carries a fine.
You can stop for a light lunch and then a more substantial dinner, or vice versa. Sometimes museums have onsite cafes that are reasonable and good. There are always the kebap places where you can get a good, quick meal for six euro or less.
Grocery stores sell cold water for less than one euro, you can also pick up fresh fruit or some other snack for a couple of euro. Remember to allow for snacks and plenty of water.
20 euro each for lunch, 30 euro each for dinner would be about right, I think, but you can do it for less. If you like pasta but want something else with it, you can usually order a half-portion (it will cost a little more than half the full-portion price). Note that ordering a coke will cost a lot more than wine, unless you get a very pricey glass of it.
Disclaimer: I once spent 60 euro on lunch. It was late, I was tired, my sugar levels were screwy, and I went for all courses: appetizer, first course, second course, dessert, wine and water, and coffee. Did not eat dinner that night.