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.

I was a ranger there last summer. Go prepared for large crowds and next to impossible trailhead parking scenarios. You'll need a pass not just to enter the park, but also one for Going to the Sun Road because visitation has gone through the roof and that road was never built with that amount of traffic in mind. Luckily, though, if you don't get a pass and don't want to deal with the trailhead parking issues, you can take the free public shuttle. It's pretty convenient and even though I lived inside the park, I'd use it to get to trailheads on my days off.

Also consider camping or staying on the east side of the park. Much quieter!

You can fly to Spokane and drive from there