Going through the park would certainly be the "shortest", but...because of traffic can be a challenge! Next best would be, down to Thermopolis, through the Windriver Canyon to Riverton, to Dubois, across Togwotee Pass, then on into Teton Park. If you don't take the Yellowstone route, Thermpoolis has some pretty good stuff ( Wyo. Dinosaur Museum, river rafting through the canyon [ if not too late in season], Hot Springs State Park, and great trout fishing in canyon to town [ guided or do it yourself]). Then the drive across Togwotee Pass is quite pretty country as you parallel the Wind River.