Welcome von.
Can't answer much as far as the medical facilities in those three towns. But for 10 years (all of 80's) I did spend a hell of a lot of time in all of them on business - usually at least once or twice a month for a couple days to a week at a time. So I do know quite a bit about them (all of western MT) if you'll ask some specific questions.
Just for a quickie to get you started...
Bozeman is cattle country, with excellent hunting and fishing opportunities and big enough for good shopping and services - and close proximity to Livingston with plenty more of the same. Close to my old elk hunting grounds near Nye, and to Yellowstone NP. Had many great fishing trips on the Gallatin staying at Pinky's and up in Three Forks. Gets a lot of snow some winters but not as cold as the other two usually based on my winter trips there anyway. Always stayed on customers ranches when in this area.
Missoula is a college town, also near excellent hunting and fishing with good shopping and services. Hamilton is well known and not far away. Coldest nights I spent in MT those years when the wind blows though. I ued to go up Rattlesnake Creek to fish, but you could catch nice trout right in the city limits in the Bitteroot and Clark Fork when I was going there. Stayed at the Red Lion and then Sheraton when it was built.
Kalispell is a great place sitting between Flathead Lake and Glacier Nat'l Park with again lots of great fishing and hunting and the other things. Personally, I like Bigfork and Whitefish the best, or even Columbia Falls close to "K". And fishing the Swan was always fantastic. Also did a lot of hunting in this area those years. The Outlaw was my home away from home when there.
They are all a little different, but all real great places with some of the nicest people you'll ever meet.
So where would I live if moving to MT - Ennis (but no VA Hospital there pard).
HTH,
Larry