Loooking for places to stay/eat/see frm Tucumcari -Nashville- Glacier, MT

That is quite a trip.  I think you should probably do the accommodations yourself as there are too many variables as to how long you are driving and how much you are stopping for me to pick. 

But here's my advice about a route.  From Tucumcari I would head east to Amarillo and Fort Worth to see the cattle drive.  You could stop and see The Mustangs of Las Colinas and go up in Reunion Tower for lunch.  Then had farther east to Shreveport  and head for Hot Springs where you can visit one of the old bath houses (free national park).  We stayed at the Baymont there.  Then you can go through Little Rock and visit Little Rock Central High School National Historic Site and the capitol.  I'd spend a couple of days in Memphis.  Even if you don't visit Graceland you can take a city tour and watch the ducks come down the elevator at the Peabody hotel and hang out on Beale Street, ride the trolley and eat BBQ.  On the way to Nashville we stopped to eat in Hurricane Mills and I think the place was called the Log Cabin

I have no advice about Nashville as I didn't like it there but be sure to visit the Hermitage (Tennessee)

On the way to St. Louis you might swing through Sainte Genevieve which was founded in 1735 by the French Canadians.  In St Louis there is the Arch. I have not been through Kansas City (Missouri) but you will probably want to go up to South Dakota and visit  Badlands National Park and Deadwood and the Black Hills on your way to Glacier National Park

Then on the way home stop by Yellowstone National Park and Grand Teton National Park and maybe stop by Colorado Springs on the way to Santa Fe (New Mexico)