Here's my advice in a nutshell:
1) Look at elk populations for hunt districts
2) Look at hunter success rates
3) Look at road densities and travel plans
Any unit with decent elk numbers, and some areas where you can get a mile from a road can provide you with good hunting opportunitites. For the most part in Montana, you will find elk on public land during archery season. Later in the rifle season you will have issues with elk seeking refuge on private land, but it's not nearly as big of an issue in September.
Every mountain range west of Billings holds elk. However, they will vary greatly in how steep they are, how dense the forest canopy is, how the elk disperse, and the relative hunting pressure. Some areas get hammered with pressure one year and have very little the next. That's why when I go to Montana I always have at LEAST three plans, sometimes more. Sometimes plan B might mean driving 100 miles.
Don't rope yourself in to one certain spot and one certain style of hunting without something else to fall back on because of hunter numbers, fire closures, flooding (like the Missouri Breaks last year), etc. Don't overthink it either.
The more time you can give yourself and the more open your mind is, the better your odds of success.