On Loneliness: It may in fact be easier to become isolated and lonely at Columbia than Princeton, but it's certainly not the norm nor does anyone who actively seeks friends find themself in such a situation. The problem is primarily that single rooms allow for isolation and corridor dorms for anonymity to some extent (esp. after freshman year). The solution is simple: opening one's door, going out and about on campus, joining student activities, even participating in online student stuff which is becoming more and more prevalent.
On New York: Yes, it does have more to offer than malls, clubs, bars, and internships; you will in fact be required to explore its musea and attend concerts in its famous halls for classes. And there are quite a few of each in the city, not even counting the outer boroughs. Then there are, of course, the theatrical productions, myriad art house cinemas (where movies are released well ahead of the rest of the country), and fascinating stores. Additionally, it's an interesting place to simply walk around: the abundance of immigrant neighborhoods, teeming avenues, pristine and bucolic parks...and even if one is simply after academic or preprofessional resources, it hardly gets better than the New York Public Library, reporting on New York news (as opposed to Princeton's or New Haven's) for campus publications, or researching at the Columbia-Presbyterian Medical Center.
On the Core: It can indeed be hit or miss, but most people are generally appreciative of it, if not as enthused as they were as freshmen. It honestly depends on your expectations. Contemporary Civilization will not be a Viennese salon with your friends acting the parts of Krauss or Freud. It, and other Core classes, will be a means to understanding significant works of literature, philosophy, and art. It's important to consider that class participation will generally enhance your experience, but the lack thereof will not harm your apprehension of the texts. and as for the readings: they're honestly not that bad; SparkNotes are of course available at crunch times (or always), and in the case of Lit Hum it's (relatively) faster-paced fiction.
I'll leave you with some thoughts on it from a professor quoted in the most recent edition of the Blue & White, a campus magazine:
Bulliet found that “this seemingly conservative curriculum is actually a very radical curriculum.” Its radicalism, for Bulliet, comes from the fact that it approaches its material without lectures from experts or secondary texts, under the direction of non-expert instructors left to their own devices. This approach, he believes, allows a uniquely fruitful kind of discussion that cultivates good habits of critical reading and thinking.
I think that applies whether or not you, and your classmates, were too burdened to do the reading or make pathbreaking comments; those skills emerge from the aspect of approaching the texts directly yourself.