In Missouri, the roads with single or double letter designations are basically paved county roads. They are usually in very good condition. Some are more like our FMs here in Texas while others are more like lane and a half paved roads. I've ridden many on bikes like VFRs, so a Goldwing should be fine. Their version of chip seal uses something more like sand instead of gravel. So if the road has been done recently, there may be loose piles of the sand around the edges of the lanes and near intersections/stops. Otherwise, they offer great traction!
Mo 76 between Cape Fair (just West of Branson) and Cassville is lots of fun. Just before you reach Cassville, head South on Mo 86 to Mo F. Head East to Mo 112. Head SW on 112 to Seligman and pick up Mo 37 to Washburn. Turn West on Mo 90 and run that all the way to Noel in the very SW corner of Missouri. You might try here for lunch,
https://goo.gl/maps/pT4s4aLbxxn
Backtrack the whole route to Branson. 76, 86, and 90 are some of the twistiest fun roads in the area! Very roller coaster like!
If you head East of Branson, US 160 is nice, but it can get crowded as it is the major East/West highway for the area along the White River and Bull Shoals Lake. ANY of the numbered or lettered roads heading East are fun, especially Mo H between US 160 and Mo 125, Mo 125 (from Oldfield all the way down to Peels Ferry in Ark to AR 14) , Mo Uu, Mo T, Mo 14 and 76 between Ava and Willow Springs/West Plains, Mo 76 between US 160 and Mo 125, Ar 14 from Ar 125 back West to US 65, and basically ALL of the paved roads bounded by Mo 5, US 160, US 63 and US 60. If you make it to Willow Springs, you might eat here,
https://goo.gl/maps/EjZdQ86gFnR2
A nice ride down into Arkansas would be to head East on US 160 to Mo 125, cut South to the ferry and cross Bull Shoals Lake. Stay on 125 to Ar 14 into Yellville on US 62. Head East toward Mountain Home and pick up Ar 201 going SE. Just before Ar 5, turn right onto Ar 341 (Push Mtn Road). This is a super nice road! If you are there on a weekend, be mindful of LEO presence!) Run it South to Ar 14, head East on 14 to Blanchard Springs Rec Area just before Ar 87. It is a cool park and a nice place to get off the bike for a bit and do a little easy walking. Be sure to check out the springs as well as the bath house/swimming area by the campground. It is really pretty. Then head down Ar 87 into Mountain View. IF you are there near eating time, I highly recommend Kin Folk's BBQ, and their Apple Fritters!!!
https://goo.gl/maps/ERdFfgs5Vno
Leave Mountain View and head West on Ar 66. The goal will be to get back on Ar 14 and head NW to US 65 for the run back to Branson. You have to great choices though. You can run up Ar 263 to Big Flat to get back to Ar 14. Or, even better, you can scoot a bit further West on 66 to Ar 74, run that to Marshall, and pick up Ar 27 back East to 14. Then head NW on 14. That stretch of 74 and 27 is REALLY fun. 74 in particular is just smooth and twisty with very little traffic. When you head North on 14, it is also fun, but you can get into rafting traffic near the Buffalo River. IF you are getting pressed for time or just want to get back quicker, you can just run US 65 back to Branson from Marshall, but it won't be as fun!
All the above could keep you busy for a week or more of riding, but you should easily be able to pick out three days of fantastic riding!