From the south of Montana to Whitefish.. two options:
Go west on I-90 - flat freeway express all the way to Missoula. Then Take highway 93 North to Whitefish.. pretty scenic. .mostly 2 -4 lane travel all the way. No passes really.
From Billings- it should take you about 5 hours if you just cruise through.
WIth stops, meals- rest.. it's a pretty good drive - most of the day. But it's very scenic and lots of little stops.
Other option: I-90 from Billings west bound all the way to Three Forks- north to Townsend/Helena. From Helena- Take I-15 North, several options to cut off of I-15 North, (again,pretty flat expansive driving ) but make your way to East Glacier- U.S 2 - Go west on U.S 2 - you will be on the southern edge of Glacier National Park.. Drive is very scenic, and while it's not the Going to the Sun Road- which might not be something for you if you don't like if you don't like high mountain passes, U.S 2 is very scenic and well traveled and a "easy pass" by Montana standards. U.S 2 West will take you right to Whitefish.
Both options are full day of driving from Billings.. but with many stop over locations for meals, gas, and sight seeing.