Cost of groceries in Italy compared to USA

That is difficult to do given the variety of prices due to types of foods. But for a budget I would simple price in dollars in the US and convert directly to Euro. In other words, if you plan to spend a $100 for food in the US, then it is 100 Euro in Europe. Could be a touch high but use that as a starting point.

I think the advice above is solid.

In general terms, my experience has been the bread and vegetables generally cost a bit less and chicken and cheese a bit more.

It depends on what you eat. Every year I compare the prices at Coop (a supermarket chain) in my neighborhood in Florence with what I pay in California (generally shop at Trader Joe, a California retailer chain that is cheaper than Safeway for example). I generally eat Italian style also in the US and I'd save in Italy for most items I generally buy.
For example, pasta, Italian bread, Parmesan cheese and most cheeses, canned tuna, canned tomatoes, cold cuts like prosciutto and salami, produce, olive oil, vinegar, wine and alcohol, yogurt, fruit are all generally cheaper in Italy. Certain seafood may be more expensive in Italy compared to what I pay here (but not all) but that may be due to the fact that the SF Bay Area is on the coast while Florence is not. I'm sure seafood will be cheaper in Venice or Cinque Terre. Also seafood is difficult to compare because I can't find in California the same variety of fish available in the Mediterranean. Meats are about the same, with t bone steaks a little more expensive in Italy, but other meats cheaper.
Also it will depend on the where you shop. Supermarkets such as Coop or Esselunga are cheaper than small specialty shops, especially in heavily touristy historical centers. Therefore you need to find out where a supermarket or the market (like farmers' markets) are located near your apartments.
Certain imported foods, that are not grown or produced in Italy, will obviously be more expensive compared to the US. Salmon will be more expensive than Seattle, lobster more expensive than Maine, peanuts, most junk food, soda, bananas etc. are more expensive in Italy. Certain foods that you might buy in the US may be also difficult (or impossible) and/or very expensive to find ( like maple syrup, peanut butter, Mexican tortillas, root beer etc.). But if you stick to foods that are available locally, you'll likely save compared to home (provided you don't shop at those tourist oriented specialty shops).

Thanks for all who replied. This gives me a good start on planning for the budget.

Happy shopping!

Also- you usually have to pay for grocery bags in Italy and they aren't very sturdy (if you are walking a ways back to your apartment). So I recommend bringing a couple reusable shopping bags or a backpack/shoulder bag that can double as a grocery bag.

Now we have to pay 10 cent for each grocery bag in most localities of California as well.
We are all bringing our own. Just like my parents have been doing in Italy for years now.

In supermarkets do not handle the fresh produce with bare hands. You will find plastic gloves for the purpose nearby. At small grocers/market stalls the shopkeeper will pick out your vegetables/fruit for you. If say you want a particular size, you can indicate which ones you want.

YOGURT COSTS A LOT MORE HERE!!! Vegetables are cheaper, fruits about the same. Many meats are cheaper, for instance, chicken breast in a public market can cost $3.00 for 2 portions. I've been traveling extensively in Italy for 23 years, lived here for a year, and my experience is that veggies are enormously cheaper (we pay $3.00 for a bunch of arugula in Oregon, while in Italy the same amount is about .80cents). Stay away from big city small shops in tourist areas. Go to the open air markets, or even those big ones that are inside a building (such as in Rome) You'll pay about the same or more for really quality bread (like we have in natural foods stores in the US) but the white, pasty stuff is very cheap. I like substantial bread -- whole grains, seeds, nuts. But that kind can cost $6 a loaf in Italy (same in Eugene, OR).

Yomo Yogurt at COOP (2 containers of 125g each (~5 oz.) ) cost €1.30 but they are on offer for €1.
I just paid $0.99 per container of 170g (6oz) for my Greek Yogurt. Not a significant difference if you ask me.