Realistic Spending Budget

Meal at a typical sit down restaurant (avg): €35-50 (more if seafood).
Meal at a budget trattoria (avg): €20-30
Prices on the menu don't change from lunch to dinner, unlike the US. Everything is "a la carte" (nothing extra comes included with what you order).
To save don't order appetizers (that's where Italian restaurants get you) but rather a 'primo' (pasta/soup) and/or a 'secondo' (main course). Order sparkling water, house wine or beer, not soda (which costs more than wine).
Pizza and beer is the cheapest option in Italy at a sit down rest/pizzeria.
Lunch on the go: €5-15
Do you need tours? A guidebook is much cheaper and museum tickets are not exorbitant. Don't skimp on museums or other sights, that's what you are in Italy for.
Shopping: the sky is the limit but I have friends who come on business to the US regularly who have not bought any clothes in Italy since the Euro was introduced. They all do their clothes shopping at outlets in the US. They save by buying in the US even when they purchase Italian made stuff. So buy only if it's something unique that you can't find in the US. Markets are good for cheap clothes. San Lorenzo in Florence is perfect. For a store that charges less for clothes in Florence go to "Santini" on via Alamanni across the train station.
If you travel in summer a lot will also be spent on drinking (beer, soda, water, etc.) at sidewalk bars while you seek refuge from the scorching heat. That adds up quickly.

If hotel and major transportation are covered than another 75 to $100 per day per person.

My wife and I prefer smaller cities outside big tourist cities to save on rooms. We start looking for lower price rooms but with high customer ratings and recommendations. And we look at TripAdvisor.com to see what people say.
We travel by train between larger cities. But we're quick to get a rental car to quickly see regions like Tuscany/Chianti.
We often plan to eat in restaurants we read about on this website and on Chowhound.com. But we often never get around to eating where we planned. We eat big at free breakfast, picnic at lunch and pay for only one meal daily. And if we have a kitchen in our B&B or apartment, we've been known to cook for ourselves. We simply don't enjoy expensive restaurants.
We have never figured out any easy method of budgeting day to day. We just travel frugally, and try not to miss any of the popular travel sights in the great cities. And we've been traveling Europe for the last 30 years in this manner--now slowly and relatively cheaply.

David's response is the perfect example of how there's no one-size-fits-all approach to travel. The idea of staying outside Rome, say, to save money and commuting in to see the sights would be my idea of a miserable trip. We prefer to stay as close to the historic center as possible so we can easily go back to our room mid-day for a break and so we can wander around in the evening without worrying about when to catch the last bus/train back. The time that would be spent sitting on a bus or train can be spent enjoying where we are.

We also manage to save a LOT on lodging by staying in apartments fairly often. We stayed in one in Rome near Campo de' Fiori for about 95 euros a night and another in Trastevere for about the same. The location couldn't be beat.

But clearly that approach works for David, so only you can decide what makes sense for you.

As for casual restaurants with great food, I have a ton of recommendations for Rome and a couple for Venice I could give you. PM me if you want them.

These are expensive cities to visit and I assume you will need air conditioning. I would plan on $200per day per person and that would incl only an occasional tour and no shopping except cheap souvenirs. Do your homework and budgeting with Rick's guidebk guidance. Never skimp on museums/monuments/gardens and use public transport always.
And yes that is for casual meals. I hope this is not a surprise since you will have a fantastic time in those cities.

Roberto gives the Very Best Advice! He grew up in Florence, as I recall. In Italy, they don't share a pizza. My husband and I save $$ by one of us ordering a pizza and one of us ordering a mixed salad. Neither of us can eat a whole pizza. The salads are big.
In Rome, you can refill your water bottles. The water that comes out of the many street fountains is very clean and pure! Thursday is "gnocci night" in Rome, and it is a delicious potato pasta dumpling. If you are near the Vatican, I love the restaurant/pizzeria :
Piacere Molise. I think the address is 60 via Candia. It would be considered a 'primi." course.

For good pizza all over Italy, look for "forno al legna" on the menu posted. It means wood oven! What I would give for one of those today!!!
For one splurge meal in Florence, get a good Florentine Bisteca -- Florentine steak. It's a porterhouse, you will share it, they will determine what size you need (will not rip you off), and order two sides. Best meal I've ever had! There are quite a few restaurants in Florence that serve it. Oh, they will serve it rare. Don't bother trying to tell them how you want it, and it's The Best Steak Ever!

We pretty much do what David does but we do stay in the cities we want to visit. We start using booking.com and sorting by price then looking for the highest rated hotel/b&b for the price we're willing to pay and then check on tripadvisor for a second opinion. We usually do as he does for meals and also do not set a budget. We are also frugal travelers but we pay to see those museums and other sights that we went to see. As for transportation, so far in Italy we have always used public transportation, but in other countries we have rented cars to get around. We will be in Italy in 2 weeks and will spend 5 nights in Rome (our third time). We're still debating the Roma pass as it seems that to be worthwhile we would have to visit 3 sites.

Bottom line is that it's pretty hard for anyone else to tell you what is a realistic budget. It will depend on how much/little you want to spend on a room, for food, and for shopping and how many sites you want to visit.

Roberto mentioned tours...just wanted to say we downloaded Rick's tour app on my ipod and used the St Marks Basilica and St Marks Sq in Venice, and the Accademia David/The Prisoners guides. They were quite interesting, and we def saw things that we would have overlooked. And learned that if you only have one mp3/ipod/iphone/whatever that you should have a headphone splitter instead of two people trying to use one pair of headphones. (You have to be well co-ordinated to even attempt this!).

Hubby and I aren't big or fancy eaters, so we found having a pizza or pasta was sufficient for us, eat LOTS of gelato...and yes, def don't order soft drinks - whew - that'll chew up your food budget fast!

Donna's right about Roberto's suggestions as he's right on the money since he's a native Florentine. I cherish his, and many others', opinions on travel.
Let me rephrase my idea on rooms. I prefer to stay in suburbs in a B&B or small hotel if I can save a buck. I'm not talking about staying an hour out of town. If I can save $50 per night and spend 10 minutes riding into the city center, I'll do it.

I left Atlanta 10 years ago because of congestion, and I prefer staying in normal neighborhoods rather than in loud, crowded parts of any big city.
Now getting back to the subject of travel budgets. I just try to see all the tourist sights, eat what looks good to me, and I just don't worry about how much I'm spending. We travel as reasonably cheaply as possible, and always get our money's worth. I worry about the Visa bill when returning home.