For a ten-day trip to Montana here are some guidelines and points of interest to consider.

The eastern part of the state is more of a prairie landscape. There are wide open spaces and rolling hills. The Custer Battlefield is here, as well as some dinosaur digs and a few lakes. To visit this area, fly into Billings.

Most of Montana's tourism is focused on the western portion of the state. The mountains start about in the center of the state. The attractions are anchored by Yellowstone National Park in the southwest corner (most of Yellowstone is actually in Wyoming), and Glacier National Park in the northwest corner. It is about an eight hour drive between the two. Banff is about another 7 hours, so it's conceivable to hit all three parks, but it's better to save Banff for another trip unless you have a lot of time.

For Yellowstone National Park fly into Bozeman, MT or Jackson, WY.  For Glacier National Park fly into Kalispell, MT which is 30 minutes from the West Entrance; or Great Falls which is about 2 hours from the East Entrance, or perhaps even Spokane, WA, which is a five hour drive from Kalispell.  You could easily spend the whole time exploring either park, though it is doable to see both. Decide how much time you want to spend traveling and how much exploring.  To see both parks there won't be time to visit other parts of the state. That could be significant, as many really enjoy the old west towns of Virginia City, Nevada City City or Bannack.  Another option is to spend a couple of days at Potosi Hotsprings (pricey, but a wonderful splurge for the handful of lucky guests who can rent a cabin well in advance) or Chico Hot Springs, which offers many accomodation options for all budgets.  Learn to fly fish on the Madison River or check out the route explored by Lewis and Clark.   It's recommended to leisurely explore Yellowstone and southwest Montana, then come back and do the same for Glacier and Banff (or vice versa)

If you do want to concentrate on the two parks, you could fly into Jackson, spend 3 or 4 days around Yellowstone, then drive up to Kalispell, hang around Glacier and fly out of Kalispell. Yellowstone is known for its scenery, abundant wildlife and thermal features. Glacier also has lots of animals, but it really shines in its scenery, and the famous Going To The Sun Road. The stretch in between the two parks is populated by thousands of rivers to fish, trails to hike, towns to visit, mountains to climb, hot springs to soak in, views to take in and countless other opportunities to experience the magic of Montana.

Fall is an ideal time to visit.  The crowds are down and the weather is beautiful. You will probably have cold nights and relatively warm days.  As you get into October, snow is possible at any time in the mountains, though unlikely to stick for too long. I'd lean more toward September or early October, as locations and gateway communitites and park services start to close by the end of October.  

** Note:  The original information for this thread came from the following forum thread: