I lived in Laurel (right outside of Billings) until I was 12 and I still go back there to visit family pretty frequently. It isn't my favorite place in Montana, but it isn't the worst either.
Some things I like about it: it has the biggest population in the state, so it has cultural events, restaurants, etc. It isn't primarily a college town like Bozeman or Missoula, so the cost of living isn't as high and there are a lot more jobs. It is nearby to lots of great outdoorsy stuff, mountain ranges, lakes, and so forth. It is right on the Yellowstone river and has lots of big, nice, parks.
Things I don't like very much: It is fairly conservative, like most of the state, and doesn't have the hippy-ish influences that the university towns do. The city itself isn't very attractive and there is a big oil refinery in Billings and another in Laurel.
Two of my cousins went to West High School in Billings, and it didn't seem like the greatest. The school was really big, and one of them had a pretty terrible time there (admittedly she was a little bit of a pain in the ass, but she was also sort of "alternative" and felt mistreated for it lot) but the other did not.
Weather is pretty typical Montana, a bit more moderate winters than some of the more mountainous towns though. It snows and gets cold, but particularly in the past few years it hasn't been very extreme. Summers are pretty short, but they are beautiful.
As far as vaccines go I believe it isn't too difficult to get a religious exemption in Montana.
Overall, it wouldn't be my first pick for a place to live. But for practical reasons I can see why people end up there, and why my family might at some point. Primarily because there are jobs there and its relatively affordable. It isn't very crunchy, but it is big enough that you could probably find your niche somewhere.