Beaver Lake near Eureka has some boating, fishing, good views, etc…
They’re cicadas. What are they going to do, serenade you to death?
I simply drove my sister (who lives in California) on U.S. 63 south from Jefferson City. Between the rolling hills and the fall foliage she was captivated.
Branson actually can be quite nice, but if you want less commercial, go for Eureka Springs.
Early October is normally too soon for good fall colors. In Missouri the peak is normally sometime after the 15th, while Arkansas hits its peak right around the end of October.
They’ll dive-bomb you on occasion. Not harmful, but they’re pretty big bugs and when one of those suckers comes screaming out of the night and thumps you in the head, well… it’ll get the adrenaline flowing.
Fortunately, my dog defends me by pouncing on and eating the kamikaze critters when they hit the ground.
My mother was not only from the Ozarks, she was from a small town called Ozark, on the Arkansas River. Beautiful part of the country. The town of Ozark is 35 miles east of Fort Smith, where I lived from ages 2-5. We moved to West Texas about a month before I turned six, and all the way into my adult life we and eventually I made the trip to Ozark regularly (or semiregularly) until my grandmother died. Once on a school break from the U of Hawaii, I took the future Mrs. Siam Sam to Ozark. While there we drove all around the northwestern part of the state, popping up into southern Missouri. The area really is worth your while.
Fort Smith, right on the border with Oklahoma, is a pretty little city. The old court of the real-life Judge Isaac Parker – as seen in the True Grit movies, although the scenes were not filmed in the actual courthouse or in Arkansas – have been preserved downtown, along with the jail and gallows of the period. Fayetteville is a pretty little college town, home to the University of Arkansas. I recall Diamond Cave outside the small town of Jasper. Seems to be another couple of caves nearby too.
Thanks, all! Sounds like the Eureka Springs area most fits our interests – some scenery, a few moderate day hikes, caves, and a bit of boating sounds like our speed. Will definitely check the art gallery situation as well. Might drive past Branson just to gawk, but I appreciate the kitsch warning.
Yellowstone and Black Hills would have been on the list if we were driving; are there any other significant natural areas within a day’s drive of Omaha that we should consider?
Not too far away is a replica of a WW2 Higgins boat: LINK
Also near the place Johnny Carson was raised in Norfolk Nebraska.
Also Omaha has some fine museums.
Ditto what Shagnasty wrote. Arkansas is a very, very beautiful state. Definitely underrated.
The Buffalo River valley offers some splendid hiking. Extra points if you both canoe the river and hike the bluffs above it. 
I’m from The Ozarks and I miss it terribly! Other than enjoying the beautiful scenery there are cave tours such as Fantastic Caverns near Springfield. It’s a good tour if you want to explore but don’t want to get dirty, because it is a jeep driven trolley tour.
Silver Dollar City in Branson is the cleanest theme park I’ve ever seen, not so much as a gum wrapper on the ground. There are many interesting folk art demonstrations there like glass blowing.
Many lakes and state parks are around. Bennett Springs is beautiful any time of year. Ha Ha Tonka State Park is nice and has the ruins of a very old mansion modeled after European castles. Lake of the Ozarks nearby is beautiful and has lots of shopping too. Branson has many good outlet malls if shopping is your thing. I prefer the flea markets in some of the smaller towns though.
You might also run across small town harvest festivals that time of year. Great crafts, food, and bluegrass music at those.
Have fun!
Another amusement park is Wild Water West located in Sioux Falls about 2 hours north of you. Its inexpensive, free parking, and have great water slides, wave pool, bumper boats, mini golf, lazy river, and these REALLY COOL go carts.
So a great inexpensive excursion.
I grew up in Harrison, and I’m a bit offended. Yes, I know the big news articles about that sign. (I even mentioned here in the Pit.) What it leaves out is that the people of Harrison got it taken down. The KKK probably thought they could get away with it due to the rumor. The rumor from a single event over 100 years ago, when similar events were happening all over.
And it is not the home of two KKK klans. They claim to be from here, but they both exist in small towns outside our jurisdiction. They were effectively driven out of Harrison. Unfortunately, the post office can’t keep them from having P.O. boxes here.
Even if there may be a few nearly dying people who are still racist fucks, no person of color has anything to fear coming to Harrison, let alone just driving through it.
Big Cedar Lodge on Table Rock Lake is where you need to go. It’s 10 miles south of Branson, and in my opinion you will find so much to do on the lake and at the resort, that you will have no need to go into Branson.