I'd like to be near shopping, eating, and entertainment during my 3 days stay.
The time of your visit is going to be critical in how/where you find a sub $100/night hotel. If you are looking in late winter, your options are wider than the warmer months.
Chicago has a lot of low amenity hotels in the central areas, so you'll likely find at least a discount brand for under $150 with some search time. A decent and historic option that is usually cheaper is the Congress Plaza Hotel. If you want to go 3 star or higher, Priceline/Hotwire will be your only bet in downtown as most mid-level properties average around $200 in the summer. With that said, I wouldn't recommend it, but if you are really price conscious AND want a nice hotel, you can often score around $100 at the hotels near O'Hare International Airport and take the Blue Train into the city. Train travel time is about 45-60 minutes.
Although I live in Chicago, I've found myself staying downtown quite often. Honestly I'd just use Hotel Tonight. If you're on an off-peak time you'll get a good deal. My wife and I used it last weekend and stayed at the Godfrey for $109. Usually it's in the $200-$300 range.
Use "lkendall4" in the promo code section and you'll get $25 off your first booking. (Full transparency: I also get $25 if you book something)
Try trivago.com or Airbnb to find hotel deals around $100 in Chicago. If you find you can spend a bit more, try The Drake Hotel - the location is perfect for entertainment, shopping, restaurants, Lake Michigan etc.
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$100 per night in Chicago is a hard number to hit unless you use some kind of discounter like blind bidding on Priceline or using Hotwire or you stay at a hostel, impossible if you are coming on a big convention weekend. Let me know if that interests you and I can find a few names of hostels. You might have a look at air bnb as well although the last few people I've talked to have gotten places well outside the center