It's Not the Rockies, But...
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For hiking in the spring, getting away from the mountains also means getting away from the snow. For roughly the same driving time you'd spend getting to the Rockies, you can get to the lower Mississippi River and the Yazoo Delta area which is replete with hiking sites including
Delta National Forest and Yazoo and Panther Swamp National Wildlife Refuges in Mississippi, Saint Francis National Forest and White River National Wildlife Refuge in Arkansas, and Upper Ouachita and Handy Brake National Wildlife Refuges in Louisiana. Then there are the cultural attractions in Hannibal, St. Louis, and Memphis en route.
AZBuck