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Your goals of "true American university experience" and exploring your surroundings" tend to be mutually exclusive. The big universities that offer the "American university experience" tend to have somewhat isolated campuses, while the city campuses tend to rely more on the surrounding city for entertainment, and are less reliant on university activities.

I'd say Wharton is your best bet, for its notoriety as one of the best, if not *the* best, business schools in the U.S.; and its location in the city of Philadelphia; but with more of a "campus" feel then many city universities. You'll be within walking distance (well, 1.7 km, or an 8-minute trolley ride) from 30th Street Station, and from there it's an easy train ride to New York City in one direction (or even Boston, although that's a couple more hours) and Washington, DC in the other, so you'll never run out of places to explore without even needing to get on a plane. There's plenty of public transportation: trolleys and subways (Metro) running right through campus, not to mention buses, so you can get downtown very cheaply and easily. 

I'd pick Georgetown as a second best, just because going to university in Washington, DC is such a treat. You're within walking distance of the Georgetown section of the city, which is a lot of fun (restaurants, bars, shopping etc), but public transportation to the rest of the city (monuments, government buildings, museums etc.) is limited to buses (while the Metro system in Washington is excellent, it doesn't extend to Georgetown). It's a long taxi ride to Union Station; and while you can still hop on the train to Philadelphia, New York, and Boston, you're at the Southern end of the commuting line (unlike Philly, where you're right in the middle). 

I'd pick USC as a distant third. LA is a pretty interesting city in itself, but it's not that easy to get around LA without a car, and there's nowhere else to get to without renting a car or flying. That said, it depends a bit on when you're going and how impervious you are to the cold. If you're going for fall semester (August-December) the weather will be much better at the northeast schools; but if you have to go spring semester (January-May) you might prefer USC if you're not used to cold weather (you couldn't pay me to go to Michigan in February). 

The others, well, I think if you're "stuck" at any of them, you'll enjoy the experience, so don't fret if you're not accepted to Wharton, Georgetown, or USC. I just wouldn't select them (over Wharton, Georgetown, or USC) for a visiting international student, as they're in small cities (or "middle of nowhere" towns like Cornell) without easy access to the rest of the U.S. 

The Wharton School at the U. of Pennsylvania (Penn) is probably America's best business program and is very prestigious. The surrounding neighborhood is not very safe. However, Penn is a private university (not publicly funded) and is thus much more expensive. The same is also true for USC, Georgetown, Cornell and Carnegie Mellon. Indiana U. (IU) is in the middle of nowhere (but not far from Indianapolis) and the same is true for the U. of Virginia (UVA), which is two hours from the Washington, D.C. suburbs. The U. of Michigan is in the nice (but distant) Detroit suburb of Ann Arbor. You're more likely to have the "typical" American university experience at UVA, IU, Michigan or North Carolina. The schools all have attractive campuses, friendly students and a lively social life. 

Sam Spayed gave you great advice about the urban universities, which might offer more job possibilities in the future if you are hoping to stay in the USA. But these are all good schools and should provide you with a good experience. Make sure they have an entrepreneurship program if that's what you are looking for.

think about/look into the placement assistance you might get from the various schools.  Wharton is supreme in financial study and placement, with the Ross School likely second.  If you've an engineering or computer type background, Carnegie Mellon is strong there.  [At the bigger universities, placement activities are specialized by school and you may have difficulty accessing placement services from the Engineering school on campus].  If you have public policy ambitions in your home country, consider Georgetown as well [and stay in close touch with your country's embassy].  Wharton, USC, and Georgetown are in big cities with major cultural attractions.  Several of those schools do not strike me as especially attractive or welcoming for culturally different students.  Read a LOT of reviews of the entrepreneurship programs ... I'm too old to have direct experience with them myself.  -- Grampa [MBA/CPA]  {married 32 years to Uni Professor of Education} {And I went to the Ross School myself, but decades ago now.}