6:49 p.m. on January 17, 2011 (EST)
Take I-15 North to Idaho Falls ID, then get on State Hwy 26 to Swan Valley,ID, then 31 to Victor ID, then 22 to get over Teton Pass and down to Wilson WY and across the Snake River to Jackson. Jackson is your best bet for fuel, groceries and supplies.
Then go north on State Hwy 89/26 to the Moose/South Entrance to Grand Teton Nat'l Park. This will take you to Jenny Lake. Jenny Lake is where you can hike into the heart of the Tetons. Hike the 2.5 miles hiking trail around Jenny Lake to Cascade Canyon and hike up to Hidden Falls, Inspiration Point and Lake Solitude.
Looking at a map of Wyoming? If you drive back from Jackson on 22 and cross the Snake River then take the Wilson/Moose road to Teton Village then take the Aerial Tram there, you can go all the way up to 10,400 feet on the Tram. From there you can hike to Lake Marion, Death Canyon Shelf, Hurricane Pass and Schoolroom Glacier, which is right behind or west of Grand Teton.
Here's some teaser views of the area below:

Home on the Range, Grand Teton is midsummer with a Buffalo.

From East Phelps Lake north of Teton Village looking at Death Canyon in the Southern Teton Range.

Jenny Lake from the northeast side looking at the Grand Tetons.

The Grand Tetons with the actually high point the second highest to the right without the cloud behind it. From north Jenny Lake Trail.

Hidden Falls west of Jenny Lake GTNP.

Looking down South Cascade Canyon in to the main canyon from 9000 feet which is treeline in the Tetons.

Mount Moran above Jackson Lake in mid-May. The lake is still frozen.

Camp in South Cascade Canyon below Grand Teton above looking east.

Grand Teton from String Lake Bridge just north of Jenny Lake.

Viewed from the top of Snow King Mountain looking north to the Tetons with Jackson Hole below. Shot in August 2008.
I lived in Jackson during the summers from 1980 to 2008.