Hey I've lived around Chicago all my life and have been mountain biking for 4 years now. I'm not sure where your living, so I'll give time estimates from the Loop to the locale.
1. Palos - forest preserve - very popular, a network of trails, not sure about total mileage. Of course here in IL we don't have a lot of climbs but there are some small ones here, and there is some good singletrack. Be careful about the close trails, the FPD doesn't like us much, nor do the hikers/horsebackers. This is probably 30 mins from the loop.
2. Knock Knolls - smaller network of tight, twisty singletrack. Very flat through. Small area with some bowls and stuff that the BMX kids maintain. Used to be alot of big logpiles and stuff but this is a community park so they took them out for safety concerns. Alot of walkers and kids and stuff here since there are alot of houses, so you just have to watch for them, but they are always cool. This place stays wet for awhile after it rains, its like a sponge. This is about 40 mins from loop.
(see cambr.org, Chicago Area Mountain Bikers webpage for more info on above trails)(also see http://cobamtb.org/
, they show alot of the trails in IN and WI as well as some smaller stuff around the suburbs)
4. Kettle Morain in southern WI has some great trails, alot of them, with some good climbs. Probably a little over an hour away.
5. Peoria is a couple of hours away and there are three places to ride, my favorite being Jubilee.
Even further out there is a trail called Kickapoo, which is just a one way loop, (neer Champaign/Urbana where U of I is) its a great trail but it is a cruise to get too.
There are also a ton of good trails in Indiana.
PM me if you want more detailed info. Also, check the trail listings on mtbr.com, thats where I found alot of these places.