Re: At Fort LeonardWood
The Big Piney River runs right through the Fort and offers some excellent warmwater fishing for smallmouth, largemouth, rock bass (goggle-eye), and a number of panfish species. The middle Gasconade is also very close by, and offers some of the best stream smallmouth fishing in the state, as well as fishing for other warmwater species. The Jacks Fork River is another nearby, it's a National Scenic Riverway and has pretty good warmwater fishing as well as gorgeous scenery. All three of those rivers are fairly popular float (canoe) streams.
As for trout, Stone Mill Spring is a small spring branch regularly stocked with rainbow trout near the Fort. There's also Roubidoux creek which holds browns, as well as several smaller streams nearby which have small populations of streambred rainbow trout. The Current and Meramec rivers are within about an hour and a half of the Fort, and both offer rainbow and brown trout fishing, as well as smallmouth and warmwater species in their lower reaches.
The Niangua River is fairly close, and offers trout, smallmouth, and other species. I also hear its summer bikini hatch is pretty outstanding : )
Check out the OzarkAnglers site, you may also want to get a subscription to the River Hills Traveler- it's a regional outdoors magazine which covers most of the Ozarks. You may be able to find it around Rolla, you can also find it online.
Good luck, and thank you for your service.