Lived out there for a few years. For a tourist that's not use to sucking down air without enough oxygen in it, take it slow. Many Glacier Park on the east side has a lot of nice places to see stuff too with fewer tourist's. The rumor is you are more likely to see grizzly bears and mountain goats there. The drive up pass St. Mary Lake is beautiful. Logan Pass and the Going to the Sun road are a great drive with a awesome view down into GNP. There are plenty of hiking trails off of the road, almost all are unguided, do at your own risk hikes. There are a few guided hikes, I think you need to sign up for those as they fill up fast. If you are into horseback trail rides, they are also offered at GNP.
The wife and I hiked into Avalanche Lake. We started from the campgrounds; along the Trail of the Cedars; then along Avalanche Creek to the lake; then back down. 3 miles up and then back down. Take plenty of water and some bear spray, you are in bear country and you may see some; we did!
If you want to fish it's $35 for 2 days, $66 for 10 days.
After you get done with GNP and you head west on Hwy 2 there are several small towns that have tourist shops in them. At Hungry Horse you can take a ride up to Hungry Horse Dam, nice scenic drive if you want to go all the way around the dam. It's about 4 hours long. Downtown Whitefish has a lot of nice shops and restaurants. On Whitefish Mountain they have an Alpine slide and a zip lines rides that you can hear people screaming on all the way down in Whitefish. They also have a walk through the tree tops, "just what it sounds like!" If you are into mountain biking you can take the lifts to the top of Whitefish and ride the trails back down or hike them down.
Everything at the north end of the valley is pricey but saves you the drive down to Kalispell. If you want to drive south and if you take Hwy 93 south through Kalispell you will drive pass some nice shops downtown. The original bear carver, Jeff Fleming has his shop/gallery just a few miles south of Kalispell on Hwy 93. Bigfork MT has a lot of great shops downtown.
For lodging check out Airbnb dot com, there are a lot of locals folks that rent out rooms or houses for the night/day/week/end on that site and it adds to the experience.
Post Script... Vehicle pass for GNP is $30, Yellowstone NP is $30 or you can get a Interagency Pass 1 year pass for all federal parks for $80. All MT state owned parks cost $6 to go into. $35 for annual pass.