The Richard D. Schwartz Observatory:
Run by the Department of Physics and Astronomy at UM- St. Louis, the observatory houses 14" Celestron telescope and an SBIG ST-8 CCD. Public open houses are held February-November, with an astronomy student operating the telescope and showing objects of interest in the night sky. Also check out their Facebook page!
The Crow Observatory: Located on the Washington University Hilltop Campus, the Crow Observatory is open to the public Monday-Thursday evenings during the fall and spring semesters (weather permitting).
Astronomical Society of Eastern Missouri: A St. Charles County based astronomy club, they are involved in the community through various public outreach programs and weekly public viewing sessions.
The St. Louis Astronomical Society: The main St. Louis astronomy club provides resources for finding open viewing sessions, and their monthly meetings are open to the public free of charge.
National Aeronautics Space Administration (NASA): Stay up-to-date with current missions, learn about past missions, and read about future missions. Plus, this is a great resource site for general interest in space.
HubbleSite: Dedicated to the Hubble Space Telescope, this site provides lots of information on the telescope and what it has done. It also includes a full archive of the images taken by the HST (they make great desktop backgrounds or screensavers!).