There are many great places to capture the Chicago skyline. I personally love the view from the Adler Planetarium but one of the better kept secrets is the 18th Street bridge. The area I'm writing about is between Clark Street and Canal Street on 18th street. This area is just north of Chinatown and just south of Ping Tom park (which is another Chicago secret).  From this location you can capture the full skyline as well as the Chicago river and the now defunct St. Charles Air Line bridge which is permanently up.  You can also head just west of the bridge toward Canal Street and you will get a great view of the Amtrack train station which has many tracks that lead directly toward downtown. 

If you are in this area I would also consider heading east down 18th street to the pedestrian bridge that crosses the train tracks into Soldier Field. This bridge gives another good view of downtown with Soldier Field in the frame. It is also above the Amtrack train line so you can capture a moving train in your shot if you choose. If you love to photograph Chicago and have never explored these areas, I highly suggest doing so.