The Botanical Gardens have 3 green houses with some orchids, tropicals and cacti but probably not as much as you are looking for. Their mainstay are the outdoor gardens. It depends on how much time you want to spend. Lincoln Park and Garfield Park are in the city and you will spend a few hours getting there and looking around. The Botanical Gardens are outside the city and you can spend the entire day there. The greenhouses would not take you longer than 45 minutes to an hour. There is a lovely watergarden collection with water lilies and lotus blossoms. There is also a waterfall garden that might help in the exotic tropical feel.

http://www.chicagobotanic.org/visit/index.php

Just checked. Garfield Conservatory is having a tropical show this summer. If it's tropicals you want - Garfield Park is probably the way to go.

http://www.garfieldconservatory.org/shows.htm