A good though strenuous hike near the Savage River campground starts at the Savage River bridge (a mile or so west of the campground) and leads up to the top of Primrose Ridge (also called Mt. Margaret). Dall Sheep may be found along the way or at the top:
On a large print you will notice on this sheep several black dots each with six legs. Bring mosquito repellant!
I agree the bus pass is a good idea. A few of my favorite areas for hikes are Igloo Canyon and Igloo Mountain, Stony Hill, Polychrome Pass and, near the park entrance, Mt. Healy and Horseshoe Lake:
There are very few trails so most hiking is cross-country. Have a great and safe trip!