zakatak-look into flying NW into Billings MT-the drive to the nearest entrance to YNP is about 3 hours from there. Does Southwest Fly to SLC (they don't come to denver so I am not familiar with them)? it is also closer than Boise. You can also fly to Jackson or Cody Wyoming via either SLC or DENVER-not cheap but not super pricing-best option for that is Delta to SLC and then Skywest to Cody-50 miles from east entrance.
Trip-Boise is very nice and most of Idaho is very nice in the summer!
edited to add-Mammoth is not the entrance to the park closest to Boise either-Both the south gate north of Flagg Ranch Wyoming and the West Gate at West Yellowstone MT are closer