On campus proper you have all the usual diversions: the dorms(and your hypothetical friends therein), the coffee shops(Uchicago has quite a few on campus, squirrelled away in various buildings), Frat row, and a decent number of student theatre, comedy, etc. shows(always seems to be something playing). Doc films is showing something every night of the academic year. There is also a professional theatre and two museums. At certain points, special events of various sorts occur(my favorite is ScavHunt).
In the immediate vicinity, things are fairly quiet. It's a nice enough neighborhood, plenty of good places to eat; but not too much going on. Beyond that, things get a bit seedy. Luckily, Chicago proper is an easy hop by bus, train, or elevated rail. Chicago itself is quite a nice city, with widely varied amusements.
As for people: You can find a broad range, of course, everything from deeply introverted math geeks to frat jocks; but there is a definite UChicago "type". In my experience, various flavors of pleasant eccentricity have been the rule. People are generally pretty sharp, and usually manage to be interesting in one way or another.
Life in Chicago: Generally good, with a few caveats. The campus is nice, as is the city, as are(mostly) the people. Classes are generally pretty challenging. The two main bitter jokes "UChicago, where fun goes to die." and "Uchicago, where the only thing that goes down on you is your GPA." are by no means entirely true; but you definitely do have to be the sort who enjoys academics. Also, winter hits some people hard. I'm a Bostonian by extraction, so I tend to enjoy it; but the Floridians of my aquaintance aren't looking too happy by the end. Winter is cold, dark, and windy, no question.
Classes: I've been very pleased. I've had some great professors(both intellectually and as people) and quite interesting course material. Now, the usual notes apply, as at any school: TAs in the sciences are inevitably accented and asian(I've never had an incomprehensible one; but a would-be chemist should be prepared), math TAs are always accented and eastern european. Rule of the Universe. Also: we have a core, it is relatively large. I think that the core is actually a great experience, and it has led me to take some really excellent courses, and I would recommend it generally. However, if you don't like the idea of a core, you'll spend a lot of time grumbling.
Any further questions, do ask.