Yep, some nice trout streams in the Ozarks, but the main attraction is smallmouth bass. The closest river system to St. Louis, the Meramec river system, has over 500 miles of fishing streams alone, all of it within less than 2 hour's drive from the city.
Closest public trout water is Blue Springs Creek, with wild trout, but it's a tiny creek and the fish are also very small and very wary. Next closest is the trout section of the Meramec below Maramec Spring (yes, the different spelling is correct), a floatable but usually wadeable stream with a lot of rainbows that come out of the Maramec Spring Park and stocked brown trout as well. It's rather mediocre fishing by Missouri trout stream standards, but if you know what you're doing you can catch fish. The park itself is put and take fishing requiring a daily tag...not my cup of tea but might be yours. It's about 1.5 hours or a little more from I-270. Other trout streams are farther away.
Smallmouth water is everywhere. There are small, wadeable streams, bigger streams that are better fished by floating, and bigger yet that get a lot of jetboat traffic. Stream access "law" in Missouri is reasonably liberal, in that if it's big enough to float a canoe you have the right to float it, wade it, and camp or picnic on gravel bars. Streams smaller than that are private, but some are still informally open to the public due to landowners that don't mind--but it's tough to figure out for sure if you're okay or not on the smaller creeks.
Other fish in them that are good fly rod quarry include various sunfish species that can be great fun on small poppers (the small poppers catch smallmouth, too). And the streams not only hold smallmouth but also largemouth and spotted bass.
