Many of the CG's within the park are first come, first served. Many Glacier on the east side is a beautiful CG that does take reservations. Currently they have about 1/2 of the sites reservable but by sometime in March the other 1/2 will also be come available. This is a very popular CG that books immediately when the booking window opens.
One useful took that is usually available on the NPS website is the
Campground Status page. But it has only worked very intermittently for me in the last couple of days. If you can get it to load, you can see when the campgrounds filled on a daily basis going back several years. Hopefully they will get it back on line as it is a very useful asset to plan when you need to arrive at a given campground. And as mentioned above, you'll have to drive on US 2 around the south end of the park to get from one side to the other a one cannot tow over Logan Pass.
St. Mary's on the east side goes to first come first served in Mid August, so that might coincide with when you'll be there. Rising Sun is another option on the east side Logan Pass road. Apgar on the west is a big CG with good proximity to the Visitors Center where you can catch the shuttle bus. It is worth staying on both sides of the park as they are quite different. West side (the wetter side) has more forests further up the mountain while the east side is more rugged.
If you are going during the summer months, yes it will be busy. Not Yellowstone busy, but there is far less parking so one has to plan accordingly. If you are hikers, use of the shuttle system will get you to most of the trailheads. Using the shuttle one can plan loop hikes. But popular routes can mean quite a queue when you get to the bus stop at the end of your hike. We had to wait 45 minutes when we took the Highline Trail down to the Loop bus stop. As noted, if you want to park at Logan Pass, plan to get there at 7:00 a.m.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)