1. Consider the East Side
Glacier National Park's West entrance gets most of the glory. It's closest to the airport and the towns of Kalispell and Whitefish. It's where most people live, where most restaurants are and where there are most options for lodging.
However, this does not mean you need to stay in West Glacier. Figure out what your priorities are. Are they hiking, fishing by any remote lake, river rafting and other excursions, etc.? If your priority is to hike, research what your top hikes are (depending on your length of stay) and that should help you make your decision.
2. Stay at least 1 week
There are hundreds of hikes and variations of hikes. Dozens of lakes, waterfalls, rivers to explore. Plus other activities like river rafting, horse back riding, fishing, the Going to the Sun Road. Ideally you'd have at least 6-10 full days to spend in the National Park. If you don't, make sure you research and determine your "Can't Miss List" so you feel accomplished upon leaving, not wishing you could stay and do more.
3. Check out the glaciers
Of the 150 glaciers that were once in the park, about 25 remain today. Most of them are several hours north of the parks entrance, and therefore take a bit of planning as you will not just stumble upon one in most activities. If this is a priority, ask a ranger early in your trip (or even before you pick accommodations) what some fun options are.
If the current rate of warming continues, all glaciers are expected to be gone by 2030.
4. Airplane mode is your friend
You won't have service in the park. If your phone is anything like mine (1.5 year old iPhone with increasingly unreliable battery), preserve your battery by putting it on airplane mode while in the park. With very minimal service your phone will be searching for a network and draining battery. This way you won't run the risk of your phone dying while trying to take a picture of a moose! Yes, this happened to me! Luckily a group member got the picture!
More National Parks & UNESCO Heritage Sites:
Your Beginner's Guide to Hiking Glacier National Park, Montana
5. Drink like the locals.
Montana makes great craft beer and alcohol. The Great Northern Brewery, located in the town of Whitefish (in one of the largest cities just West of the park) has a great IPA, called Going to the Sun, and an Ale, called 1933.
We also stopped at Glacier Distilling to taste their fine spirits, primarily whiskey but also gin, absinthe and vodka. We ended up taking home their Two Med whiskey.