Thats a HUGE and HEAVY trailer for that truck.......... that being said, back to the Black Hills, Badlands, Devils Tower and the way to get there.
If you take I-70 (to and thru Missouri)..... At Kansas City take 435 north and west to connect with 29. this avoids the more congested interstates further in to KC.
The one state park in MO that I stayed at, Graham Cave SP at Danville, about 60 mi west of St Louis was way too tight for a rig of your size. Cannot speak for others, but MO SP's are antiquated and they are just now in the process of rebuilding the campground in them.
Depending on your timing you might consider an overnight stop at Horseshoe Casino at Council Bluffs, IA, its right off the interstate exit 18, fuel at the interchange and is a very large asphalt parking lot with water and power hookups and showers and laundry, $40 a night but lots of room, secure and a kinda pricey buffet inside (everyone always says that casino buffets are cheap, this was not). Check-in at the security office, and must pay with a CC.
Speaking of Council Bluffs, there is always a lot of construction going on. Lots of walls, temporary lanes, zig-zags, narrow lanes, lots of bumps and humps, bordering on dangerous in places the last time I went thru there. It is clearly visible on Google Maps satellite pics which are fairly recent. Go slow thru there.
Another casino with a large RV parking area further up 29 is WinnaVegas at exit 127 Sloan, IA (about 30 miles south of Sioux City). It is about 3 miles straight west of the interchange and has about 15 RV parking spaces with power pedestals, $15 a night. Not mentioned on the web site, but it is available (99cent breakfast too!)
On I-90, about 140 miles west of Sioux Falls is Chamberlain, SD. A few minutes north of there on the Missouri River is Ft. Thompson and Big Bend Dam. There you will find Left Tailrace Corp of Engineers Campground. Extremely nice and in the middle of the Missouri River, below the dam, water on three sides. It is most easily accessed from Reliance, SD via State Rt47, which is a little past Chamberlin, taking St Rt 50 north from Chamberlain is more scenic but very hilly and might be a little un-nerving with a big rig.
By all means visit the Badlands, even if you have to backtrack to it after you park your trailer somewhere. There are a couple of RV parks in Wall, SD at the west end of the Badlands.
The route that Busskipper shows thru Nebraska, I have driven every inch of that same route, eastbound, last August. Nebraska highway 2 is a good route, good pavement. I stayed at the Nebraska Nat Forest at Halsey, on my return, there are a few sites that would accommodate a large rig, and its just off the highway. Very scenic, wished I had more time to spend exploring the trails and river there at the campground.
Backtracking a little on Busskipper's route, at Mahomet, Illinois, on I-74, exit 172, about 3 miles west of Champaign, just a few feet off the exit is the Museum of the Grand Prairie. I spent a couple of hours in there one day and didn't have time to see it all. Again, if you are into museums, if not....
http://www.museumofthegrandprairie.org/At Chadron, NE, if you are into museums, is the Museum of the Fur Trade. Its about 3 mi east of Chadron on US 20. Its good size and very interesting, well worth a couple of hours.
Here is my recount of my Black Hills, Badlands, and Eclipse trip of August 2017. It may provide you with a little bit of info or links you might find useful.
https://www.rv.net/forum/index.cfm/fuseaction/thread/tid/29487108.cfmI am very glad I was able to take one route out, and a different route back, more scenery to see, things to do, etc. Had it not been for the eclipse, I may have not gone thru Nebraska.
Charles
'03 Ram 2500 CTD, 5.9HO six speed, PacBrake Exh Brake, std cab, long bed, Leer top and 2008 Bigfoot 25B21RB.. previously (both gone) 2008 Thor/Dutchman Freedom Spirit 180 & 2007 Winnebago View 23H Motorhome.