You're staying in a great, central location (although parking will be difficult and expensive). Gary and I are planning to get away to Chicago late April for about a week, and we finally decided to take the train and leave the car because once you get there, a car is sort of a liability, especially if you're planning to stay downtown rather than taking day trips to the outlying areas. I'd recommend that. You'll probably end up spending about the same as you would for parking. I lived there for 25 years, and once Gary and I finally left just a few years ago, the city traffic had turned into pretty much 24 hour rush hour traffic, which is one reason we wanted to finally move.
I dunno whether four days is enough to do justice to Chicago proper and any outlying excursions. And for sure the Wisconsin Dells is farther than I'd prefer to go myself, given the relatively short trip. Chicago traffic has become exceedingly overwhelming over the years, and it's really a major pain getting around in a car.
[I've just googled travel from downtown Chicago to the Wisconsin Dells, and it's roughly 200 miles, which certainly seems right to me, from what I recall.]
I'm pining to get there (we'll be staying in roughly the same area) so I can get out and walk. Chicago is one of the best walking cities on the planet, and really walker-friendly. And it's as easy to grab a cab to get from one place to the next, should you need to.
Depending on the sort of fun you want, you're going to be just a few blocks from Navy Pier, and if the weather's amenable, it's wonderful to get out and walk to the pier and along the lake. When I lived in Lincoln Park, I used to walk for miles and miles and miles, all along the lake between Lincoln Park and down town (the gold coast, etc). You could walk there, if you want a nice long walk, or take the el, which runs maybe ten blocks west of there. The Lincoln Park Zoo is one of the nicest small zoos you'll ever find, I think. And it's right next door to the very beautiful Lincoln Park Conservatory and also the North Pond restaurant. Walk west toward Clark street or Lincoln Avenue and you're in the heart of the the restaurant, bar, shops and theatre area in Lincoln Park.
Either direction north and south and you're sort of along theatre avenue (small theatres off loop and beyond), including Second City, Goodman, Royal George, Steppenwolf, Victory Gardens.
Head just north, and you're in Wrigleyville (or "Lakeview"), still more or less on the lake, with more off-loop theatre and Wrigley Field, an area that's famously known in Chicago for its strong gay community (also known as "boystown) and where they host the massive gay pride parade every year. Some particularly beautiful architectural landmarks, Temple Shalom (on Lake Shore Drive and Cornelius) and Our Lady of Mount Carmel.
And of course from where you're staying, you're surrounded by theatre and restaurants and clubs and bars and beautiful archetictural artifacts. Just walking over the bridge is interesting. The Sun-Times and the Tribune buildings are gorgeous. The Water Tower is there (including Water Tower Place just across the street). You're surrounded by Frank Lloyd Wright, Louis Sullivan (see the Carson Pirie Scott building), Mies van der Rohe, Daniel Burnham, Helmut Jahn, Frank Gehry (Millenium Park). And then there's the Picasso at the Daley Center, the Chagall mosaic at Dearborn and Monroe streets, and the fabulous Cows on Parade, the precursor to Louisville's Gallopalooza.
You'll be right in the center of the blues scene (The Back Room, Buddy Guy's, Blue Chicago, B.L.U.E.S., Andy's). And one of my favorite places, Pops for Champagne, though I've only been to the original in Lincoln Park, not to the one down town (or out north). If you want to catch a cab, the Green Dolphin is sort of cool, a big cave of a place, upscale.
You'll be within walking distance from the Art Institute, the Museum of Contemporary Art, and (a longer walk) the National Vietnam Veteran's Art Museum in the south loop. Cab's distance from the Field Museum and the Museum of Science and Industry, also favorite places.
If you're interested in Frank Lloyd Wright, there's a nice walking tour in Oak Park (where I was born), the suburb just adjacent the west side of Chicago.
Wicker Park and Buck town, also west of down town and Lincoln Park, are sort of hotbeds of nightlife in an area that is still going through some serious rehabbing and renovation. Off-off loop theatre, good restaurants, small clubs. One of my favorite little restaurants just around the corner from where Gary and I lived on Wicker Park, Cafe Absinthe at the intersection of North and Damen but which you enter through an alley just behind the corner tavern. May be more fun with several folks at once.
Just west of down town is Greek Town where you'll find great Greek food everywhere. The Printer's Row area just south of the loop is a newish area with interesting historical architecture and some good, small restaurants. You'll be too early for the massive book fair in June, but it's a nice place to wander for a bit. Just west of there along Canal and Roosevelt Roads is the famous open-air Maxwell Street market.
But something more to your liking may be the Randolph Street/Fulton Market area. The Fulton Market used to be the really run-down meat packing district with a big open-air market where we'd go to get fresh fish and which has recently been transformed into the newest hot spot for galleries and clubs and restaurants (Blackbird, for example). Here's an interesting story from TNYT:
http://travel2.nytimes.com/2006/12/03/t ... acing.html.
You'll have to stay a month....
[eta: I see we've all been offering pretty much similar advice all at once.]
