You can bring food and hike. I have backpacked for multiple days throughout Yellowstone and carried food with me. It's just a day hike--you need to eat. I wouldn't hang a fish from my pack...but I would be fine with cheese and crackers or a sandwich. Bring bear spray--clipped to your belt--and know how to use it. There are some very good books--Best Day Hikes series for Yellowstone, Grand Tetons, and Glacier. Check out the ww.nps.gov website for each park. They have descriptions of all of the hikes and talk about difficulty and elevation gain, etc. June will still have plenty of snow at higher elevations. When we went to Glacier, Going to the Sun Road did not open until after July 2 that year--you just never know. I think the museum in Cody is amazing--keep that in your back pocket if you get a super rainy day--that's what we ended up doing.