The main thing to know is Glacier is a zoo the last several years. If you want to park anywhere you need to arrive early. The days are long. You need bear spray unless on a ranger-guided hike and they are pretty cool especially to areas like Dawson or Firebrand Pass in Two Medicine led by Pat Hagan who is from the area and has lived there for many year.s His stories are awesome https://www.amazon.com/Seasonal-Disorde ... B01K3KQKZU
I'd say for a first-timer the Highline Trail is a must. However, if you are driving your car to the Logan Pass VC, you must go early as it fills by 8:30 AM. Otherwise, I advise to take the Park Shuttle and leave your car at St Mary VC. It would be around 14 miles if you did the out and back; does not include the the mile spur trail up to the Grinnell Glacier Overlook if you want a good touch of AEG. You can also do it as a Loop but The Loop Trail is pretty steep: http://www.hikinginglacier.com/highline-loop.htm
You can do the hike down the Swiftcurrent from there but the logistics are tricky. And of course, if you like AEG, doing the SCurrent trail by itself is a beauty. http://www.hikinginglacier.com/swiftcurrent-pass.htm
The Siyeh Loop is another good choice where it goes from Siyeh to Sunrift Gorge. Once again, you will need to use the shuttle or if you plan on parking, go early. They say with the shuttles it's best to start with the shuttle and then hike to your car so you don't have to worry about time constraints. I think this loop is 10 miles. http://www.hikinginglacier.com/siyeh-pass-loop.htm
On the Many Glacier side, as Chumley indicated, definitely do the Grinnell Glacier hike if you can. Hopefully it will be clear enough to get to the glacier itself but if not, it's still a good hike. You can make this hike longer or shorter depending if you use the boats; which incidentally provide awesome rides but they aren't cheap. http://www.hikinginglacier.com/grinnell-glacier.htm
Once again, you need to get there early to get parking above the Many Glacier Lodge. And of course, Iceberg Lake with a side trip up to Ptarmigan Tunnel (make sure it's open) is a beauty too and gives you that AEG you're looking for if you do the Tunnel. This one you would park at SCurrent Motor Inn. http://www.hikinginglacier.com/iceberg-lake.htm
If you pick up this day hiking map from Jake https://hike734.com/hiking/
, you will get a really good idea of all the hikes you can do along with other info.
I'm headed up there on the 24th with Wendy. We are backpacking in the Cut Bank area on the 26th to Pitamakan and Triple Divide Pass (you would probably like the Triple Divide Pass as it's got some nice AEG and the destination is pretty great). And after we get back from that we are headed to Granite Park Chalet for a couple nites.