So are you making Mena your stop over for the first night? If so, check out the TWT Sponsor section for the Ozark Motel. Very biker friendly.
Unless you have two days to ride from there to St. Louis, I would recommend riding a bit farther the first day so that you have time to really enjoy the second day. If you split it in half, 375 miles does not sound like a lot for one day. However, if it is all twisties, then it makes for a long day, particularly if you are not used to long days on the bike.
I'd shoot for Russellville at a minimum. Clarksville would also be good. You can run Hwy 123 NE from Clarksville, to Hwy 7, then hit 16 over to 27 or 377 up to Marshall (food/gas). That route is a BLAST. From Marshall, take 27 East to 14, stay East to Hwy 341, also known as Push Mountain Rd. If you are there on a weekend, watch for Park Rangers and Sheriff's Deputies as that is a popular road because of the fun factor. Run that North up to Hwy 201 and then on into Mountain Home. A fun side trip that might take you about an hour extra is to run up Hwy 123 to Mt Judea and back. MAJOR twisty with very little traffic and excellent pavement. Definitely worth the effort if you can fit it in. You could even run up 123 all the way to US 65, head South a bit to Hwy 235 then 125 and keep going East all the way into Mountain Home.
If you are feeling good, Mountain Home is actually a good place to stay on your first day out. It really depends on what time you try to get away from the DFW area. If you can leave in the morning, it would make a good long day ride. There is a Best Western there in town on US 62 Bus., where I usually stay when I take groups up there. Very biker friendly, clean, decent rates, and they let us park the bikes under the covered walkway. There is a real good steak house about a block up the road in easy walking distance and a booze shop across the road if you want/need that
If you plan to pass through Mena, then run 71 up to Hwy 28, 28 to 27, and then run 27 all the way up to Marshall. Just for reference, it would be about 240 miles from Mena to Mountain Home if you run up 28, 27, 14 and Push Mountain Rd.
Out of Mountain Home, I would head East on US 62 to Salem and pick up Hwy 9 North to Mammoth Springs. This is another nice ride. 62 is not technical so will be a good warm up for getting on the bike in the morning before the fun stuff. Also, you want to get around West Plains. As the name implies... it is just flat plains. At Mammoth Springs, US 63 North to Hwy 19. Run 19 up to Winona. From here out, anything between Winona and St Louis is generally going to be a fun ride. There will of course be less traffic on the minor roads. I don't know if you are up for any unpaved roads, but there are a zillion of them in that area! I'll highlight two potential routes for you.
Route 1 out of Winona. Stay on 19 North out of town all the way up to Hwy A. Head East on A to Bunker. Or... if you are feeling adventurous, just before you get to A is Cc. Cc is a small loop. Midway into the loop is CR 250B off to the right. This then runs along a ridge roughly parallel to A as CR 2221. It will eventually become Cr 565 and run on into Bunker. From Bunker, head SE on Hwy 72 to Hwy KK. Run KK up to Hwy 32, go East to Hwy 49 and then North to Hwy Y (might also be labeled C). Head North on Y to Huzzah. Head East on Hwy 8. Now again, you can say on pavement or chance unpaved
You can stay on 8 to Hwy AA, running AA to 185. Or... you can go about 3-1/2 miles from where you get on 8 to Berryman Rd. Hang a left (North) and run up to CR 250, go right (East) until you reach Cr 2265. Continue East until you reach AA. Go a little over 2 miles and look for Fourche Renault Rd., on your left. It may also be labeled Cr 211. Run this up to 185. At 185, head North to Hwy T, hang a right and run up to Hwy A, hang a right again, run to Hwy 47. Head North on 47 to Hwy FF (stay right), run up to Hwy 30. Run 30 East on into St. Louis. That is about 275 miles from Mountain Home to the outskirts of St Louis. LOTS of twisties!!
Route 2 out of Winona. Just North of Winona, hit Hwy H and head NE. Run it up to Hwy 106 and head East. Look for Hwy B on the left, BEFORE you get to Ellington. Head North on B until you reach Hwy 72. Go East on 72 to Hwy 21. Run 21 to Hwy 49, go North on 49 until you reach Hwy 32. Go East on 32 to Hwy DD and go North. Hang a right on C and go a short distance to Hwy P, continue North. Follow P to Hwy 8, hang a right and hit Hwy 21. Follow 21 on into St Louis. This is about 250 miles from Mountain Home to St Louis.
If Mountain Home is just a little far, Marshall has a few "Mom & Pop" type hotels. One is right on US 65/Hwy 27 on the South end of town. Nothing fancy. Cheap. And a good restaurant right across the street. Gas is found on the North side of town. There is not much between Russellville and Marshall, except great riding!