Make a point to get into western Montana - You can't go wrong. I've got some friends that live in Whitefish (north of Bozeman/Missoula). It is amazing country and there are countless opportunities for exploration. You'll likely find yourself in a remote area at some point in your trip, so be sure to bring some extra gas with you, as "necessities" can be scarce.
My advice would be to purchase a Montana Gazetteer (available for pretty cheap on Amazon, etc.). This will give you basic maps of all roads and trails for a given area. Once you figure out what area you'd like to explore, contact the local enforcement agency (USFS, DNR, BIA, state timberlands, etc.) for additional information.
Glacier National Park is not to be missed! If you have the time/interest, plan for at least one day hike somewhere in Glacier. The trail to Grinnell Glacier out of Many Glacier on the east side of the park is an exceptional day hike! You can enjoy a sneek peak by "Googling" Grinnell Glacier. If you elect to camp in the park, plan ahead: there are times of the year when campsites are VERY scarce. You can book campsite reservations on-line.
If you find yourself in the Whitefish area on a Friday night, the Resort at Big Mountain offers free round-trip chair lift/gondola service to the summit. At the summit you will find a couple of bands, a full-on Bar-B-Que spread, friendly beers, and AMAZING views (to include a birds-eye rignt into the west side of Glacier NP). Again, if you've got the time...
Great trip - I don't expect you'll be disappointed!