Sorry if Ralph and I rained on your parade, but the reality is that there's no way you are going to be able to hike mountain passes in late May and early June. In fact, you may be limited to valley day hikes along the fringes of the park as it's highly unlikely that you will be able to reach the heart of the park via the Going-to-the-Sun Road. The chances that it will be open all the way through are practically zero.
Click the link below to see a map of the park's roadways. Note how much of the GTTS Road currently is closed. By the time you get there, you may be able to go as far as Avalanche on the west side and Jackson Glacier Overlook on the east side. The odds are that everything else in the middle will still be closed.
http://home.nps.gov/applications/glac/r ... status.cfm
If you still want to camp, several of the front-country campgrounds may be open when you arrive but may not have much in the way of services yet. Visit
http://home.nps.gov/applications/glac/c ... status.cfm as your arrival date gets closer to see which sites might be open for you.
Also, most of the park's lodging, restaurants, etc. will still be closed when you arrive. Glacier Park Lodge on the southeast side and Lake McDonald Lodge and the Village Inn on the west side will be open, but everything else will still be closed. Swiftcurrent Motor Inn in the Many Glacier region is scheduled to open on June 3. I don't know the opening dates for lodging or restaurants just outside the park. See
http://www.glacierparkinc.com/ for more info on park lodging.
You'll want to keep all of this in mind as alternatives if you are unable to do any backcountry camping.
Valley day hikes that you can probably do will include:
- Avalanche Lake (west side) (6 miles round trip and mostly flat)
- Swiftcurrent Valley (7 miles round trip to the headwall of the pass in the Many Glacier region on the east side)
- The lower portions of the Iceberg Lake and Grinnell Glacier trails, along with Grinnell Lake (Many Glacier region) (varying lengths depending on how far you can go, but nothing more than 7 miles or so)
- Hikes around Two Medicine Lake in the Two Medicine region (southeast area) (varying lengths)
- Red Eagle Lake (east side near the St. Mary park entrance) (15 miles round trip, but flat all the way)
Hope that's not too much of a downer for you, but it is what it is. Let us know if you have additional questions.