My partner and I will be in the same area around mid-June (we are driving from Portland)!! Neither of us have been to Grand Teton or Yellowstone before, so our to-do list is really long. Hopefully we will have enough time! We definitely want to visit Amphitheater Lake, the Cascade Canyon Trail, Willow Flats, Firehole Falls, the Teton Crest Trail, and the Grand Canyon of Yellowstone. This website has a ton of information: http://www.enjoyyourparks.com/GlacierYe ... nPark.html
For food, we are bringing lots of granola bars, carrots, avocados, tofu jerky, apples, nuts, dried fruits, peanut butter, bread, oranges, and whatever else we find en route to the parks.