What kind of things are you interested in doing while you are in The Park? Climbing, hiking, backpacking, wildlife viewing, wildflowers.....?
I'm a Glacier Park addict, so let me know your interests and I'll try to help with a plan.
I visit the park year-round, but my favorite times are the fringe seasons, when the crowds and the bugs are gone.
You will most likely want to visit after the Going To The Sun Road opens over Logan Pass. The pass can open anytime from late May to early July. But the last several years it has been opening in late June. This is partly due to the construction projects going on.
Here is the park web site-Glacier National Park (U.S. National Park Service)
And here is a Glacier Park discussion forum. This forum is not real active at this time of year. But you can search around the site and find some really good info. This site has some of the kindest most helpful people I've met on the internet. Glacier National Park Chat • Index page