What are the best vacation destinations within driving distance from Chicago?

This former Chicagoan is a big fan of Door County. I especially enjoy the northern tip, Gill's Rock area.

I was going to suggest Niagara Falls! It was a mere 8 hours from Chicago, and so much fun. You can go romantic and get a nice big room overlooking the falls, or you can go cheesy and get a cheap hotel in the "strip." It's Vegas Lite!

I'm in Milwaukee. For a shorter trip, my vote is for Washington Island at the tip of Door County. You have to take a (car) ferry to get there. There are B&Bs and quaint little shops and nice views of Lake Michigan. Depending on how outdoorsy and athletic you are, you can bring/rent kayaks and kayak to Rock Island. (Or hire a boat.) There are no roads there, so you'll have to hike in and camp and shit in the woods. If you don't want to drive too far and you have a decent budget, I'd stay at the American Club in Kohler and wrap yourself in luxury. If that's too pricy, stay at the Inn at Woodlake next door and have dinner at the Club. It's seriously romantic and luxurious.

Oh, yeah. Someone mentioned wine country in Missouri--check out the http://www.bikekatytrail.com/, if you like to go bicycling. You can even do a little bike touring, if you're so inclined--ride during the day, visit the wineries, stay in B&Bs in towns along the way at night. Lots of nature and a nice crushed-limestone path. May is a good time for something like this. And our favorite of the state park lodges in Illinois is http://www.pmlodge.net/, which I actually prefer to Starved Rock. There's actually quite a lot to do around Alton and the Illinois/Mississippi confluence--lots of parks and wildlife refuges, little towns to explore, museums (http://www.greatriverroad.com/cities/ealton/rivermuseum.htm). And this is an incredibly good time to visit http://www.carmitimes.com/topstories/x481350614/Learning-the-secrets-of-southern-Illinois-Snake-Road in the LaRue/Pine Hills area of Southern Illinois. (Also, salamanders, lizards, turtles, and frogs!) We live in central Illinois, and one of our favorite things to do for a mini-vacation is to justhttp://www.southernillinoiscabins.com/, cook our own meals, and hang out in the woods for a little while. Last--this is a little farther, probably about 7 hours for you--no one has mentioned the http://www.lbl.org/ in far western Kentucky. They have a herd of bison (including adorable babies) who frequently wander into the road en masse and stop traffic, and elk who are a little more elusive, but there. There's a museum and a planetarium. There are also a lot of state parks in the area, including Lake Barkley, http://parks.ky.gov/parks/resortparks/lake-barkley/default.aspx.

The Keeweenaw Penisula in the UP is quite beautiful.

As a displaced STL native I will second (or third) that suggestion. Also not on your list, and a bit more rustic, is http://www.doorcounty.com/ -- outdoor activities as well as lots of artists. I also just drove back and forth through Cleveland twice this month -- a 7 hour drive and in the same class of destination as Milwaukee and Indianapolis. It is an easy drive, but apart from saying that you'll need to find your own attractions there.

Superior National Forest and the Boundary Waters Canoe Area Wilderness in the Arrowhead of Minnesota are within driving distance, I made the trip in about nine hours a couple years back.

Seconding Madison, where I live. If you come at the end of May you can go to http://www.wiscon.info/, which has got to be nerdy enough for you. We certainly have all the cultural sites you describe, though none of them on the scale of Chicago.

Duluth MN is about 8 hour drive, small city, a mecca of Outdoorness lots to hike and explore, decent food (plus you know, Lake Superior), added bonus I've give you a tour gratis, and can hook you up with someone who will give you a tour of local commentaries.