I lived in Glacier for two seasons working on a backcountry trail crew. I've hiked 75+% of the trails in the park and have favorite hikes. I've been asked to give suggestions on good hikes before, so rather than type up a whole new suggestion list I'm going to paste some e-mail correspondence below.
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Trip One - "The Northern Traverse" - 7 days, 6 nights This trip consists of 7 - 10 +/- mile days and will allow participants to experience the entire Northern span of the park. It brings you up and over both the grueling Stoney Indian Pass as well as the mellower Brown Pass (the continental divide). As a means of reference as to the difficulty of this route, I did this route in three days and two nights last summer, averaging 20+ miles per day. It recommended as a 5+ day hike, so to do it in 7 would allow time to appreciate the scenery and relax in camp.
Day 1. Hike from Chief Mtn. Ranger Station (Northeastern corner of the park) to either Cosley or Glenn's Lake campsite
Day 2. Hike to the gorgeous Stoney Indian Pass campsite
Day 3. Hike to the Goat Haunt area (can't remember the names of camps here).
Day 4. Hike to the Lake Francis campground which is in my opinion the first or second best campsite in the park.
Day 5. From Lake Francis, climb the mellow Brown's Pass switchbacks, and head to either Hole-in-the-Wall or Boulder Pass campsites. Boulder Pass is the other "best" campsite in Glacier. Even the toilet (an open air "low-rider") provides a spectacular view of the Whitefish Mtn. Range.
Day 6. Drop down the pounding switchbacks to either the camps at Upper or Lower Kintla Lake.
Day 7. Finish the trip by hiking out to the Kintla Car camping area.
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Trip Two - "Coal/Nyack Loop" - 6 days, 5 nights
This is considered the ruggedest route in Glacier in that it encompasses many (low water depth) stream-crossings and is in the remotest section and least visited part of the park. The trip begins and ends with a ford of the Middle Fork of the Flathead River and begins and ends with forested walking. The middle days of the trip are filled with expansive views of high peaks and passes as seen through the remains of the all-encompassing fires of 2003. The trip stays to the valley floor except for one almost imperceptible crossing of Suprise Pass.
Day 1 - Begin at the Coal Creek Trailhead (get precise directions from a ranger or use the Shuttle Service), ford the Middle Fork and hike approx. 6 miles the Lower Coal campsite.
Day 2 - Hike another 7 to 10 miles through trees and one or two fords to Upper Coal creek campsite.
Day 3 - From Upper Coal you'll head into the burn of 2003 which allows amazing views of the surrounding peaks and in particular, Mt. St. Nick (a Matterhorn-ish looking peak) until you come to the Martha's Basin area. The campground is at Beaver Woman Lake and this hike is approx. 10 miles.
Day 4 - Cross the easy Suprise Pass and continue hiking through the burn until you arrive at the Upper Nyack campsite.
Day 5 - Hike to the Lower Nyack campsite.
Day 6 - Return to the trees and hike out, fording the Middle Fork again and once again entering civilization.
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Trip Three - "Dawson/Pitamakin Pass Loop" -
This is a very short trip that many people do as a long day-hike. It starts and ends from the Two Medicine area of the park and one can actually catch a scenic boat ride rather than hike the first half of the first day.
Day 1 - Hike/ride the boat along Two Medicine lake and then ascend to the No Name Lake camsite.
Day 2 - Climb Dawson pass and proceed along a ridge and sidehill to Pitamakin Pass and then descend to the Old Man Lake campsite.
Day 3 - Hike back out to the Two Medicine Area
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These are rough descriptions of three routes. I highly suggest cross-referencing the routes I described with both a park map as well as a guidebook (if you have one). I only had my memory and atopo map to create those scenarios so I don't remember that many mileage figures. I haven't hiked the Dawson/Pitamakin Loop in its entirety but I've done the other two routes (the Coal/Nyack loop I've done three times). Like I mentioned before, feel free to nit pick with questions, as you may be able to tell from the lenght of this message, that I don't mind helping out.