Kalispell is the closest airport, but it's expensive. I flew into Missoula and did some extra driving. The drive was beautiful.

You need to get off going to the sun road (def need to do a drive through) and do a hike. Preferably over one the many passes. I skipped the more popular trails and did Siyeh pass and it was mind blowing. Glacier Backcountry is amazing, but it is also more accessible than a lot other parks (Yosemite, north cascades come to mind). The best thing, of course, is to do a backpacking trip. There is no bad trail in Glacier. Just get any permit (or a walk up) and your jaws will drop.

I went there in 2013. If you like mountains, Glacier is a heaven.