Being from Chicago I figure I should chime in.
Friday the 25th, the Taste of Chicago starts in Grant Park, however we've been having some really crazy storms lately so I am unsure if you'll be able to get anything.
I also suggest walking down the "Magnificent Mile" which is Michigan Ave. You should also find Wacker Dr. (NOT LOWER WACKER) and take pictures of the Trump Tower and Hotel, the Marina Towers, the IBM building etc.
Basically Michigan Ave, State St, and Wacker Dr are some good spots to take pictures of buildings. Also maybe if the weather is nice, go on a Lake and River tour. They cost about 25$ per person.
Also if you're into Fireworks, weather permitting, Saturdays and Wednesday at Navy Pier (A place you should also visit) has 15 minute Firework shows at 10:15PM (Sat) and 9:15PM (Wed).
You should also visit the Sears tower (It was renamed Willis but it will always be Sears to me) and go to the Skydeck and try out "THE LEDGE" it's basically a glass box that extends out the window and allows you to look straight down.
Also if you arrive on Thursday in Millennium Park, right now is Party in the Park which means a couple of bands play for FREE every Thursday.
Also don't forget the other park, Grant Park. Near the back end there is Buckingham Fountain.
Sadly you are not coming the month of July. Transformers 3 is filming here and that would definitely be something to peep.
Hope that helps.