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Try to get through Jackson Hole and the Grand Tetons. It's one of my favorite places and the mountains will just take your breath away.
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This guy knows what he's talking about. ^^^
Jackson is only about a 15-20 minute drive to Teton National Park.
Once in TNP, you can take a small ferry across Jenny Lake, which drops you off at some trail-heads. From there you can take one of the most breath taking day hikes this country has to offer. Absolutely stunning. Make it what you want....a couple hours, all day....whatever.
Also, in the early morning, if you drive north a few miles outside of Jackson, there are a ton of meadows where you'll routinely see elk and moose wandering around shallow streams. The wildlife out there is just amazing. Grab some breakfast for the road, some coffee and spend a few hours soaking in an epic landscape.
I've done a ton of traveling both in the U.S. and over seas. Teton National Park has very few rivals.