I agree... you're a bit early unless you're visiting someone or working there. A LOT of snow this year!
Take 89 north from Flagstaff, AZ to UT I-15 to I-80 at Evanston, WY. Then 89 north to Jackson..... 1,022 miles
Explore Grand Teton Nat'l Park's web site to stay up-to-date on road information and campground openings if planning to stay there.