Hey dude,
NZ is on the list of countries in the visa wavier programme, so no. If you travel after 01 12 09, you’ll need to register on a usa government website before travel but before then you’re golden.
Stuff to do in the windy city…hmm. Loads of museums; art, natural history, many world class. History Museum a definite goodie. And there’s the Sears Tower too…the usual ridiculously expensive place to drink and dine from above.
Plenty of clubs as well (it’s the home of House after all!) I saw Derrick Carter when I was there in ’03.