We're 90 minutes from St. Louis so I'm no help on places to stay, but our favorite places to visit are:
St. Louis Science Center
http://slsc.org/
St. Louis Zoo
http://www.stlzoo.org/
Grant's Farm
http://www.grantsfarm.com/
Magic House
http://www.magichouse.com/
http://www.explorestlouis.com/visitors/ticketsDeals.asp "TICKETS & DEALS To make your visit to St. Louis even more fun, informative and inexpensive, click on the logos below to learn more about special offers through our promotional partners."
Edited to add more:
World Bird Sanctuary
http://www.worldbirdsanctuary.org/
Lone Elk Park
http://www.stlouisco.com/parks/LoneElk.html
Missouri Botanical Garden
http://www.mobot.org/
All the visitors centers in Missouri have brochures for the entire state.