Over the past few years, miles of new bike paths, bike lanes, and bike signage have been added throughout the City. The reconstruction of ten miles of the Mississippi Riverfront Trail will be finished this year. Forty-seven miles of bike paths will be completed by the end of next year. And all of this does not take into account existing trails in Forest Park, Tower Grove Park, and other places.
With the price of gas going through the stratosphere and the weather turning so good, now might be a good time to use some pedal power.
Here is a link that will help you find the trails/lanes:
Trail/lane map of the City
And here are links to a couple of good bike shops: