I second ppzcgg's suggestions

NE & SE entrance are truly nice. But be sure to find out when those entrance close before you get out the park.

I got out NE entrance and went all the way to Cody and come back at SE entrance - watched sunset at the Lake.

If you drive from Salt Lake to Teton, be awared that one can't go ~40mph along a large portion of Hwy 89. If I remember correctly, it took me ~8 hrs from Salt Lake to Teton and had to skip Jackson Hole (Teton's last boat to Inspiration Point at 6pm, almost missed).

Plan 2hrs before sunset and drive from Teton to Old Faithful, you may be able to see Old Faithful eruption at sunset, beautiful!