If I had to make a choice between Teddy Roosevelt NP in ND and Glacier NP it would be Glacier hands down. I’ve been to all the areas mentioned. If you go to South Dakota, Custer SP, Wind Cave NP, the Blackhiils, Mt. Rushmore, the Badlands NP, and back over to Devil’s Tower is a must and they are all close together. Keystone is the town closest to Mt. Rushmore and has some restaurants to choose from.
Teddy NP would be an out of the way afterthought not as spectacular as the SD Badlands. Both to us were drive by and see. Too desolate to want to stop. Near the Badlands is Wall, SD and Wall Drug for a FREE glass of water is a must. [;)] When I was a kid during the 50s bumper stickers were on cars everywhere for that free glass of water. [:D] If you want to go to Teddy NP there are two separate areas to visit. The southern one is right off the freeway and near Dickenson if you need a town to stop in. The other northern branch is about as remote as you can get.
The next time I am in that area I want to stop at Pork Chop John’s in Butte, MT. If you do go to Glacier the Going to the Sun Road is an absolute must. If you go west on it you can go on into Whitefish and there you should find some good independent eateries.