The closest commercial airport is 65 miles north of Rye Creek Lodge in Missoula, Montana(MSO). Driving time from Missoula is about 1 1/2 hours.
Butte, Montana(BTM) is also a possibility at 117 miles and is about a 2 hour drive.
Spokane, Washington(GEG) is a 4.5 hour drive from Rye Creek, and a better airfare can sometimes be found there. The drive from Spokane is very scenic and is 190 miles on I-90 and 65 miles on US-93.