The bars in Italy (yes, they call them bar...imported foreign words tend to stay singular, even in the plural) are quite different from the bars in the U.S., and maybe in your country, too. Think English pub. Without the cute.
They are places where the whole family can go, where people drop in for a quick espresso (if you must, caffè lungo, caffè americano -- American-style coffee, but, if you want to fit in, don't embarrass yourself by asking for a cappuccino after breakfast time), a quick bite or lunch, and, later, an aperitivo (aperitif, pronounced ah-pair-ah-TEE-vo), and even a Happy Hour, but typically no heavy drinking goes on, here.
What's there to eat?
For breakfast, pasta frolla (a wonderful usually S-shaped sugar cookie) or brioche/cornetti of all kinds (pronounced bree-OSH / kor-NEH-tee): semplice (pronounced SEHM-plee-chaye with the "ch" of "church") with nothing inside, or with cioccolato (chocolate, pronounced cho-ko-LAHH-toe, with the "ch" of "church") or marmellata (different flavors of marmelade, jam; pronounced mar-meh-LAH-tah).
For lunch, there are typically cold sandwiches called panini (pronounced pah-NEE-nee; singular: panino ... instead of "nee" at the end, add "no") with all sorts of stuff inside, toast (UNTOASTED sandwiches on soft white bread), or piadine (plural, pronounced pee-ah-DEE-nay, for the singular add "no" on the end, instead of "nee"): a thick flour tortilla-like thing that is filled with stuff, and then just folded over. They'll ask you if you want it heated on a grill (Da riscaldare?). Sì for yes, and no for, well, no.
If you want it to take-away, say Da portare via (pronounced dah poor-TAR-ay VEE-ah), and they'll put it in a little sack for you. Don't forget your manners: per piacere (please; pronounced pair-pee-ah-CHAIR-ee) and grazie (thanks; pronounced grah-ZEE-aye).
Want something sweet, afterwards? Torta (a kind of heavy flat cake, pronounced TOR-tah) or frutta (fruit, pronounced FRUU-tah) are typical. Or a gelato (pronounced jeh-LAH-toe).
Oh, before we finish the bars...sitting down, even if you take your cup yourself and bus the table yourself...usually adds a Euro or two to the price, so you'll have to get the feel of individual bars before you do it. Servizio a tavola (table service) always costs a few Euros more, and, no, you may not sit down at those very inviting tables under those shady umbrellas without ordering something.
Some bars, or even cafeteria-style restaurants, have pre-prepared cold food that they can reheat in a microwave. In Milan, these typically are pre-prepared or choose-your-own plates of the following: verdura (vegetables, pronounced vair-DUR-ah), patate (potatoes, pronounced pah-TAH-tay), arrosto (roasted beef or veal, pronounced ah-ROH-stoh), cotoletta (veal cutlet, breaded or unbreaded, pronounced koh-toe-LEH-tah), and pasta (PAH-stah). There may also be uova (eggs, pronounced wu-OH-vah, singular irregular: add "voh" instead of "vah").
This is like a half-way stage between a cafeteria and a tavola fredda. It's usually in a bar with more generous seating, and they have a sneeze-guarded area with heated food ready for your choosing; it's not self-service, you'll have to ask for what you want. If you're picky about your food, since it has been kept hot (and usually goes pretty fast, so relatively freshly made...particularly important for avoiding soggy pasta), it usually is a better taste choice than the preceding options.
This is a chain of cafeterias owned by Autogrill (see below). It's one step above the tavole calde because the high turnover keeps some of the typical stuff fairly fresh (although I still recommend avoiding the pizza and pasta, as it's not at its best), while other things are prepared for you right in front of your eyes (for example, very tasty grilled chicken breasts). Salad fixings are fresh, but you'll have to be content with oil and vinegar for dressing (I recommend getting out of the habit of other kinds of dressing that cover up the taste of the salads and add useless calories). Keep an eye on what you put on your tray. It can add up.
An Italian pizza chain belonging to Autogrill (see below). What can I say...bleh. Avoid it. Pizza restaurants are plentiful, the costs are reasonable, and the pizza is MUCH better.
If you are driving in Italy, these "pitstop" places mix bar-tavola fredda-tavola calda-shop (and bathroom amenities) for a break. As you might imagine, it's not the best you'll ever have eaten, but it's the only thing available pretty much, and is certainly better than nothing. Besides Italy, they are in a few European countries and even North America. Want to find out more about them? Here's the website in English.
WORD TO THE WISE
Before you go, at least look up the stuff you hate, or can't eat, but keep in mind that Italy is just now awakening broadly to vegetariansim or to special dietetic needs. You'll need to be flexible, and explore. That is, after all, what travelling is all about. Even at the table.
Remember, I get no kickbacks of any kind for mentioning restaurants and shops!