I've fished the wilderness southwest of Stanley, Idaho, for about 15 years. Lots of excellent fishing, but a significant hike to get to the best fish. We've ventured into the wilderness on foot as far as 20 miles from a trail head carrying ultralight 4 lb float tubes (Wood River and Wilderness Lite), waders, fins, and fly gear along with food, shelter, and clothing for a week. Highly recommended; an outstanding destination. One caveat--last September several of the areas in the vicinity of Stanley--and elsewhere in Idaho--experienced significant forest fires. So, suggest you check with the forest service before you finalize your plans for 2014.
In a typical year the trails in the Stanley area above 8,000 ft are passable on foot beginning in mid, sometimes late, July. I've been there the second week of September and been hit with snow. It is a short season. You mentioned bicycling, and of course, the wilderness is limited to travel on horseback or on foot only; no mechanized vehicles are permitted. Have a blast.