I'm not sure whether you're referring to the W Lakeshore or W city center. Either way, the rates seem pretty high. I assume you're not a AAA member? It's just that there's a pre-paid 21 day advance purchase rate for AAA members at the W City Center, and that brings the rate down to 179 or something like that.
You mentioned 6/12 to 6/15. If you can stay till 6/16 (ie a 4-night stay), you can take advantage of the buy 3 get 4 offer and stay at the W Lakeshore for 289 a night for the first three nights and then fourth night free. That works out to under 220 a night. The offer is prepaid and nonrefundable, though. If you are interested, you can find the offer here (KathyWardf was first to bring this to the forum's attention, I should add) : http://www.starwood.com/promotions/p...?promoCode=X4O

There's always something going on in Chicago, and summer time is especially popular for conventions etc.

Good luck!