Only about 70 miles to the border, about 100 miles to Jackson Lake, but it will take 2 or 3 hours to drive because of the 40mph limit, winding roads, and even longer if you stop for the sights (like Old Faithful).
Grand Teton National Park is in Northwest Wyoming just south of Yellowstone National Park in a place the mountain men called Jackson's Hole or Jackson's Valley, now just known as Jackson Hole.