If it's open check out the Sky Chapel. It's a church downtown that has a chapel up on the 22nd floor.  
The architecture boat tour is fun and cool.  
If it's in service take a short ride on the Water Taxi, from near Union Station to Michigan Avenue. It is interesting to see the city from the river.
If you enjoy architecture check out The Rookery Building and the lobby of the Marquette Building. There are walking architecture tours in the downtown area.  
The Japanese Garden in Jackson Park is beautiful.
And, of course, a picnic lunch at Northerly Island is a pleasant way to spend some time.

Outside of the traditional tourist traps, I would recommend

The Hubbard Street Murals - nice neighborhoods, safe, and will keep you busy for an hour or two.

If you don't take a boat tour, take a water taxi - they will take you from Michigan ave to Chinatown (then check out Chinatown)

Lincoln Park Zoo

Go to 2122 North Clark Street, there is nothing there but that is the site where the St Valentines Day Massacre occurred even though the wall is in a museum in Canada.

Take an elevated train around town, Green line/brown line, ride over the river. There are some great scenic shots from the train.

Walk down the stairs at Union Station, where they had scenes from The Untouchabes.

The Hilton on Michigan Ave, has a decor inside that is historic and looks amazing.

Walk into City Hall, they maintained the look from the 1920's

Viagra Triangle - thats good people watching when its busy.

Chicago River Walk has nice seating and restaurants to watch the boats on the river.

Macy's (ahem, Marshall Fields) on State Street. You can check out the cathedral ceiling, and other cool stuff they did on the "history floor)

The green line of the Chicago "L" runs both east-to-west and north-to-south.  Avoid the north-to-south leg.  Not much to see south of the loop away from the lake, and the area may be less welcoming than it once was.

Stop by the Wiener‘s Circle in Lincoln park. It’s a hotdog place go after midnight and Ask for the chocolate shake

The Lake Street (east-west) leg is only marginally safer, and that's because its terminal is in a good neighborhood.  Unless you want to see the Frank Lloyd Wright architecture in Oak Park, there is no good reason to ride the Green Line in the first place.