We just came back from a weekend trip. This would be an excellent multi day route to Glacier through the best parts of Montana. We camped at the National Forest Campgrounds south of Red Lodge (Parkside, Limber Pine). Then you do the Beartooth Highway and cross over the northern end of Yellowstone (Lamar Valley) without actually staying in Yellowstone (one day trip). You gotta do Beartooth once in your life. Avoid though if you have a big rig or take an extra pair of pants and make sure your insurance is up to date.
You can head north to Gardiner or keep going and head north through West Yellowstone as you get ready to head north. Discovery Center in West Yellowstone is worth checking out for the bears. There are some gorgeous national forest campgrounds heading up to Bozeman from West Yellowstone. They even have electricity now days. Red Cliff stands out and it is right on the river. You can fish with a license, walk fifty feet and cook them in your fire pit. Split em, gut em, pack em with garlic and butter and wrap in foil, 10 13 mins a side, hmmm. Also get a smoked trout from the Beartooth cafe in Cooke City and put on ice for a light snack or lunch, hmmm. If you like IPAs', check out all of the MT ones. They are almost all good. Recommendations are Bent Nail (Red Lodge), Tumbleweed or Single Malt (Helena), Shake a day and most others.
From Gardiner or West Yellowstone, it is about three hours north to Helena. Take 12 across Helena and head north at Avon do a few miles on 200 and north past Seely Lake. At the top of McDonald Pass west of Helena is a very nice wooded campground Cromwwell Dixon or you can keep going. Head North at Avon up past Seely Lake to Glacier. This whole drive from Helena to Glacier is one of the most beautiful in the country in my opinion. There are National Forest and state campgrounds along the way also but usually full.
Once you get to Glacier area, I'd look at the KOA or Glacier Campground about a mile south of West Glacier as a base for doing Glacier. Take your passport and go to Waterton in Canada if you have a few days.
Other alternatives are to head from Black Hills cross over on 14 to Cody and head north and across the northern end of Yellowstone. You will catch the end of the Beartooth Highway. You can do 14A and hit the Medicine wheel. It's all good.
