Restaurants in Italy come under various headings, and are not all just plain old "Ristoranti". You'll find "Osterie" and Trattorie" too, as well as "Pizzerie" and "Enoteche". Traditionally, the osteria and trattoria were cheaper and more popular alternatives to the smarter ristorante. However, this is not necessarily the case any more and it is probably more helpful to have a look at a menu and peer through the window to see what a place looks like! White linen tablecloths often indicate a smarter, more formal, and therefore more expensive restaurant, but not always, as this kind of table linen is also indicative of simple traditional cooking.
The term Osteria is quite trendy these days, so it may not always indicate a cheaper place to eat. A trattoria, generally speaking, offers traditional informal dining. Pizzerie of course speak for themselves, but they often offer meals other than pizza too. An Enoteca or wine bar will usually still serve meals, but there will be a very good wine cellar too. Italians don't normally go out to drink wine without something to eat, and even the sparkling prosecco often served as an aperitif will be served with some kind of savoury snack, even if it's just a few peanuts!