You want to learn Italian. You used to think there's only one variety—standard Italian—you can learn, right? Unfortunately, that's not the case, just as there are plenty of English, French, Korean and Russian varieties. There's formal Italian, old-fashioned Italian, familiar Italian and that incredibly rich and original Italian spoken by youngsters, with local differences depending on the region. And the Italian they speak in Switzerland doesn't entirely overlap with what Italian pupils are taught in school. Further, the languages to which you're exposed when listening to the radio or watching TV is also not representative of how "Italians speak". Language is, in fact, the sum of multiple languages.
As a student of German, I experience this firsthand: the dilemma of choosing which German upon which to focus. At school, they inevitably teach you the best German possible, with the highest and most elegant linguistic standards. That's usually what students expect, right? To be taught how to speak properly, with the so-called educated and cultivated population.
Unfortunately, though, this "noble" language is neither the language you need to chat over dinner with friends, nor when you talk on the phone with others, and not even when you ask for directions on the street. Therefore, write down your own goals before you start learning a language: what do you need it for? Making friends, living abroad, or enjoying literature and elegantly-written newspaper articles? Whatever the case is, ask your language tutor to provide you with the appropriate tools to dive into the language you want to learn (rather than the language they think you should speak).
Help your teacher to understand your goals and have them tell you how you can use the language they teach you. As far as Italian is concerned, for example, there are many dialects and jargons, and some of them can be much more interesting than standard Italian. If you're the kind of student who wants to talk like the Italians do and make friends on the road, during a summer trip in Sicily or Tuscany, ask your teachers how things are said in Italian AND in dialect.
Locals will immensely appreciate your interest for their peculiarities and will invite you for a coffee or dinner at a typical osteria. Just keep in mind you may not understand much of what they say after a beer or two. However, sometimes, just training your ear to differentiate different accents and pitches is more important than learning new words and speaking perfectly, "as a printed book" (as Italians say).