While I-15 is the fastest way to go the 1,400 miles from the east side of Glacier NP to San Diego and goes past lots of nice NF land to the east in Utah, along with Bryce and Zion NP, you might consider an alternate route if you have more time.
National Parks during the high season aren't as much fun. We're having a better winter to date than 2013, which means that Glacier NP will have lots of snow in the high country and on the Going to the Sun Hwy. The predicted opening of June 20, 2014 for the highway may slip. It opened June 21, 2013 and the Logan Pass Visitor Center parking lot had 8 foot walls of snow at that time. Hope you are here in late July or August.
For the trip to SD consider staying closer to the eastern front of the Rockies on Hwy 89 until it merges with I-15 is prettier than Cut Bank to Shelby and the 15. Further south consider cutting over to Hwy 93 by taking US 10 (SR 1) past Georgetown Lake then SR 38 to Hamilton to pick up 93S for more very nice country. You could take Hwy 93 all the way to Las Vegas, yet there are lots of smaller state highways just to the west that provide even more experiences. At Challis, ID head west on SR 75 along the Salmon River to Stanley, then SR 21 to Boise, I-84 east to Mountain Home then south again on SR 51 and other roads to get to Elko, NV. Then back route it to Ely, then finally to LV and the 15 to SD
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