We live south of Houston, and have traveled up that way many times, with and without our RV.
Same route, regardless.
We take 288 to I-59 the Harvey Toll Road in Houston, then 45 to 287 in Ennis, then 287 all the way to Amarillo. We pick up US-87 there. It's possible to skirt Amarillo, RVTW should direct you.
From there, Trip Wizard wants to route you through Channing, WHY, I don't know. Narrow, remote country road with no shoulder. Don't do it!
We've always taken 87 north from Amarillo, to Dumas (left turn), Hartley, all the way to Raton, where we pick up I-25. Several beautiful rest areas from Trinidad to Cheyenne.
There are several options after that, so here's some comments:
We try to stick to Interstate highways, (we're a motorhome towing).
If we can't use an Interstate, we try to a US highway, 4-lane divided. But in Colorado, Wyoming, Montana, sometimes those are only 2-lane,, but good enough.
Houston, Ft. Worth, and Denver are no fun - be sure to time your passing through, to avoid rush hours. We just follow the route RVTW lays out through Ft Worth (no fun, watch signs, review in advance)
North of Denver, in Ft Collins, RVTW might route you on US-287 to Laramie. It's a scenic, interesting drive, decent road, but not fun for a motorhome towing going through Ft Collins downtown, so we go through Cheyenne instead.
I can give you our routes through Wyoming and Montana, but there are few options, and we had no issues with RVTW routing - it's pretty rural, and desolate in many places. Good roads. Few large cities. Wyoming and Montana are quite sparsely populated. Few places to stop and eat, or get fuel or groceries, and there's those darn mountains to contend with

.. plan ahead.
- Places of note: Ayres Natural Bridge - county park in Woming - beautiful, peaceful, free camping, We would love to camp there, but 30 ft RV limit and absolutely NO PETS, can't even leave them in your car.
- (There's also a great county park in Shelley Idaho (North Bingham County Park) , if you happened to come back that route, as we did).
- We almost always stop to pay respects at the Ludlow Massacre Memorial between Trinidad and Walsenburg, a mile or so west off I-25, well marked (RVTW takes a weird route which we ignore and just take the Ludlow exit). Lovely place, good interpretive display, plenty of turnaround space, parking in shade is possible. The Ludlow ghost town is just south of the memorial, but in ruins.
We have taken several different routes through Wyoming and Montana and had no significant issues anywhere, except for finding places to eat breakfast, once.
I do strongly recommend three resources:
Google Earth to scope out roads and camping,
Rest Area app - great resource - lots of good rest areas on 287 between Fort Worth and Amarillo.
Road conditions websites: IMPORTANT: find a website for each state (they differ) to check road conditions especially construction which can delay you considerably. There is a stretch between mantras in Gunnison under construction that is extremely rough, and we lost a snap pad there (fortunately still under warranty, and they sent a replacement). there are no reasonable alternative routes and there are many 18 wheelers that take that route, even though part of the zone is VERY bumpy, hard-packed mud.