I'm not going to be as pleasant as David. Quite frankly, anyone who thinks that Paris is "boring" is a tasteless, illiterate, half wit.
(And as nice as Chicago is there is no comparison of its museums with those in Paris.)
Paris is a town that is open all night. Many clubs stay open till sunrise. (Bars rarely check IDs by the way) There are people constantly in the street. There are venues for every type of music imaginable.
The food is fabulous. The women are beautiful.
Mainly its Paris. This is the place where people like F. Scott Fitzgerald, James Joyce and Hemingway used to hang out. You can go to a place like the Cafe Procope, the oldest cafe in Paris, and sit in the same booth that Thomas Jefferson and Ben Franklin sat and had a glass of wine. You can hang out at Le Mazet where Jim Morrison had his last drink.
You can walk the streets and see the locations where dozens of famous movies are set. You can walk on streets that Roman legionnaires used to walk or have a cup of coffee at the Cafe de Deux Magots where Jean Paul Sartre held forth.
You'd be out of your mind to go anyplace else.
You want something specific to do?
Join the least exclusive club in the world. The Café Metropole Club meets every Thursday afternoon. To "join" all you have to do is show up. Read about it here: http://www.metropoleparis.com/aclub.html
Try the Friday night skate thru the streets. read about it here: http://www.pari-roller.com/index.php?p=101
Have Sunday dinner with an icon of the 1960's free love, hippy, movement. Jim Haynes is still crazy after all these years. An American he helped organize the Edinburgh Fringe Festival, co-founded "Suck" (a magazine about sexual issues) in Amsterdam, and taught Media Studies and Sexual Politics at the University of Paris 8. He holds a dinner party every Sunday night at his atelier. Read about it here: http://www.jim-haynes.com/