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Current River.  There's a reason they made it a National Scenic River.  The upper sections (Montauk to Akers Ferry.) have excellent trout fishing, are very scenic, and can be "sporty" kayaking.  I like to put in at Tan Vat Hole and float to Cedar Grove for a nice day float with great fishing.

eta; The upper Jacks Fork River (Also in the National Scenic Riverways.) has great smallmouth bass fishing, is very scenic, sporty, and flows into the Current River.  The lower sections are not as scenic and are the only portions with cabins along the bank.

I have done more than my fair share of floating Missouri streams and those are my favorites.  In fact I'm heading to the Current in the end of July to camp, float, and fish.
 

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So I'm heading up to a farm around Macon County (Kirksville?) for the 4th of July and will be taking my time getting back to Texas.  I plan on hitting the 11 point River, and then Bull Shoals and Mulberry river in Arkansas.  I'm looking for a national/state park with good fishing in Missouri.  Any recommendations?  I will be solo, with a kayak and sleeping in a hammock.

ETA

Looking for places to target fish that I can't in Texas, so walleye, pike, trout are on my wishlist, but good smallmouth waters are intriguing as well.

The Gasconade, probably named for French settlers from the province of Gascony in southwestern France, is reputed to be one of the most crooked rivers in the world. Entirely within Missouri, the river winds nearly 300 miles from its source near Hartville to the Missouri River, which is an airline distance of about 120 miles. In an area near Waynesville, you can float for 15 miles and be only two miles overland from your put-in.

Dru Pippin describes the Gasconade well in The Rivers of Missouri when he says, "...steep bluffs, gorgeous cuts, hairpin turns, and lazy eddies; hardwoods, softwoods and dogwoods, hidden logs, protruding boulders that weathering has tumbled from adjacent cliffs, wildflowers and shrubs, birds and bees, four-legged creatures quenching their thirst at my water's edge, while listless white clouds float above as though convoying my trip."

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I like around Pineville, MO and staying at Kozy Kamp.  For a more energetic trip, take the Big Sugar down to the camp.  For more leisurely, take the Elk from the camp down to Noel, MO.  The Big Sugar flows into the Elk.