Thanks guys!
July would probably be the busiest time anywhere, let alone GNP. This was in early September - after Labor day, and I was surprised how many people were here, despite the bad weather. I suppose I was here also... so..
It certainly is a must-see. The closer you can stay to the park the better I would assume. It was a bit of a trek each day from Somer, MT to GNP, but not too bad for the Western side of the Park.
For the Many Glacier area, if you want to get on the trails early and do some hiking, You might end up staying on the Eastern side of the Park somewhere. Some Holiday Inn Express etc in Browning I think.
EDITED - To add - While I mentioned Browning, I have no experience staying there. When I was in the area of the Blackfoot Indian reservation, I felt uncomfortable and on edge, and couldn't wait to get out of the area. The Holiday Inn Express idea came to my head, because a friend of mine mentioned he stayed there and it was OK. This friend is a earthy hippie type. So YMMV.