Eastern Montana is HOT and is more "badlands scenic". Miles City (on I-94) has a nice KOA if you need a break. I'm a lifelong resident and have lived in the east and the west - I would recommend getting to Central/Western Montana to spend your time. If you go across the Hi Line (HWY 2 across the north) you will have to get past Havre to find some nice camping. Lewistown in Central Montana is very pretty and there is a lot of dispersed camping in the Belt Mountains - west of Lewistown toward Great Falls. For camping there go to the Lewis and Clark National Forest website. If you're coming on the Interstate - get to Laurel (just past Billings) and head south to Red Lodge. Or continue on toward Big Timber, Livingston, Bozeman. For these areas go to the Custer-Gallatin National Forest Website. Further West and you'll have to navigate some mountain passes - but Butte is very historical and Missoula is a great college town in the mountains.
Most of all - it's a HUGE state. Take your time and enjoy our lack of Sales Tax!