I also recommend staying in an air b&b. I'd stay in either the Loop (the downtown area with all of the big buildings) if you like continual action and lots of activity, or the Northside (lots of neighborhoods to choose from, from the near-north neighborhoods closer to the Loop, to Lincoln Park and even Lakeview, where Wrigley Field is). If you're into walking, you can literally walk from Wrigley all the way to the Loop. It's probably about 7 miles or so, and is nice stroll for the day, where you can take your time and get to walk through a lot of interesting neighborhoods that have lots to offer. Stay close to the "L" (the elevated train). On the Northside, you can choose either the Red line or the Brown Line. The Brown line is nicer, IMO, and both lines stop relatively close to one another. The Red line is more convenient, though. Both go to the Loop, with the Red line going much further south.
To add to things to do:
- Go to a brewery, of which there are a plethora of just in the city itself. Just do a little research, and you'll most likely find a couple that will interest you.
- Do an architectural tour of the city via a river boat. There are several different companies that run tours. They're relatively inexpensive, and they are fun and informative.
- If you're into cycling, rent a bike and ride along the Lakefront path. Go south, and once you get beyond the Shedd Aquarium, it will be much less crowded. You can ride almost to Indiana, but for a moderate distance ride, I'd recommend riding to Hyde Park, where you could drop in to the Museum of Science and Industry. From the Loop to Hyde Park should only take you about 1 hour (more if you ride slowly), and the path is entirely flat. The only problem may be the wind.
- If you are interested in seeing an old baseball stadium, go see Wrigley Field. Even if you don't see a ball game there (which will most likely be sold out, anyway), you can walk around the outside and get glimpses of the interior (and do lots of people-watching/film-shooting).
- Go to the top of the John Hancock building (just recently named something different) and have a drink at the bar. You go there for the excellent views, nit the bar, but for the cost of a drink, you can hang out and enjoy the view(s) of the city.
Hope you have fun if you come (and I'll be visiting in your home country at that time). Chicago is a great city to visit, especially in the summer.
JP