During hunting season, one has to work a bit to see the critters. And the closest strips to the critters are some of the busier ones for hunters. In addition, some airstrips might not be the ones you may or may not want to go to right away on the first trip in, but,.....
From Soldier Bar, the access along Big Creek offers good fishing, great views of the Creek, the Gorge, petrographs and glyphs, teepee rings, access to the Middle Fork, and good camping upstream along the Creek. For the intrepid, the ridge from the strip offers access towards Dave Lewis peak, where goats occasion. The east fork of Rush creek offers an entire drainage pretty much to yourself and away from the hunting camps. Lots of elk, and numerous moose. Sheep are found mostly on the north side of Big Creek..the best places for seeing them butt heads are the benches at various places above 4800' or so...above Taylor, around Horse Mountain, up Cliff Creek, and directly above Soldier Bar up towards timberline to the north. The spring lambing cliffs are to the northeast overlooking the Main and Middle Fork.
All of the above can be found up to the head of Waterfall Creek, which takes off at a nice grade right above the Big Creek/Middle Fork confluence.
The area is pretty hot and dry for me in the summer, and is still dry in the fall. Numerous springs can be located with USGS quads and paying attention to the usual animal signs. Few trails are depicted or maintained in this area away from Big Creek, but there are old trails from even more than 50 years ago that make the going pretty good for most of the suggestions given above, and outfitter trails elsewhere.