Never too early to plan! :cool:
Chicago always does the fireworks on the 3rd - so they will be Sunday night. The racing at Red Bud ends around 5 pm EST and the Chicago fireworks start at 9:30 pm CST. That gives you 5+ hours to get from Red Bud to Chicago, parked, and a seat somewhere on the lakefront. The drive with no traffic should only be 2 hours max, but unfortunately I-80 sucks and sometimes has terrible traffic coming back into IL from the MI/IN area, as well as the traffic coming out of Red Bud after the 250 2nd moto (we usually leave with a few laps to go - and take a shortcut out of the track).
Okie is right, the Chicago fireworks are something else and I would definately check them out. Over 1 million people gather along the lakeshore for the display with over 5,000 fireworks used. The Taste of Chicago runs June 24th-July 4th in 2005 - something else worth checking out if you'll be in town for a day. Red Bud will have a fireworks display Saturday night (and probably Friday night) as well, it's good, but no Chicago.
If you're staying overnight while at Red Bud (I would definately attend Saturday-Sunday) then Niles is the closest town with hotels (15 mins away) but the rooms book up fast.