Hmm...my old stompin' grounds....if you like hangin' at parks, the system near the lake is awesome, whether Grant Park downtown or Lincoln Park on the North Side (closer to N'Western). Lincoln Park has (or had) a free zoo you can walk around. . .
Also, River North has some trendy sports bars, etc. . .though you can find that kind of stuff all over the city, but there are some microbreweries around on the North side, too. Your girl might know somethin' about those places. If you go downtown, hit up Marshall Field's if you are into browsing, or take a long walk down Michigan Avenue and see all the trendy stores. Make sure your girl has lots of money to buy you stuff.
If she really likes you, ask her to get some reservations for Second City (I think it's still there in Old Town. . .been a few years but you can check on that). There are several improv and comedy clubs that you can sometimes get cheap tix for around. And Dan Ackroyd and Jim Belushi have a Blues club - I think that's on the Near North side.
If she's got a car and you are on the cheap, just drive up the lakeshore north of Evanston and check out the awesome Bahai Temple. Or take LakeShoreDrive south toward downtown - great views.
If she's got connections, make her take you to see Da Bears at Soldier Field. . .or a N'Western football game (they are Big 10). And if you get a free eats day, hit up Pizzeria Uno or Due or see if Leona's (one in Wicker Park, one in the west burbs) is still doing their awesome Sunday Italian brunch buffet. . .(casual place.)
Oh yeah...make her get you tickets for Jerry Springer...hehehe..or dammit - Oprah - maybe she'll be givin' everyone a new car again that day...