New to Glacier national

I just recently got a job and started buying up lots of lightwieght gear (although I think I have a ways to go)to go to Glacier park in Montana. Ive never been there before.

Can anyone here recommend any good trails or hikes for my 8 day trip? I really like the sound of the Dawson/Pitamakan hike but the permits for August are all taken. (What would happen in me and my friends camped in the forest without a permit?)

Thanks!