A long but non-technical day (or overnight) climb to one of the northern Beartooths' three highest summits, following the Granite Peak approach partway before splitting off toward Mount Hague's own plateau.
From the West Rosebud (Mystic Lake) Trailhead, follow the trail along Mystic Lake's south shore to its western end and cross the log-jam over the outlet to Island Lake, where flat camping areas make a good base for an overnight trip. From camp, head roughly north toward the drainage between Mount Hague and Mount Wood, then climb steep slopes -- mostly open, with little bushwhacking compared to other Beartooth approaches -- to gain Hague's summit plateau. The last mile and a half is an easy walk across the plateau, with expansive views of Granite Peak, Mount Wood, Villard, and Glacier Peak; the true summit lies toward the plateau's northwest side and is not visible from Mystic Lake itself.