There are many state and local parks in Montana that don't fill up except on holiday weekends. Get a state parks pass. I haven't explored the state as much as I'd like. I usually do my trip after school starts in the fall to avoid the crowds and visit stuff in Montana on the way to or from Yellowstone.
Official State of Montana Vacation, Recreation, Accommodations and Travel Information Website
National Park Service - Experience Your America
US Forest Service - Caring for the land and serving people.
I seam to have lost all my links to places in MT. Need to find them again. The state has lots of lesser national and state parks and forests.
Check the fishing regulations. For the national parks you may need both fishing permits for the park and state. I don't fish, but I remember something about that.
In Glacier NP the main Going to the Sun road area is often filled, but northern and southern ends have spaces available. Also you can make reservations online.
If you haven't been to Yellowstone, it is worth stopping. If you do visit Yellowstone,
enter or ext via the north east entrance road and go over the
Beartooth Pass. Just make sure the weather is good that day. Storms can be real fun up above the tree line. One evening I went over it and they had the big snowblowers sitting there idling at the turnouts. That wasn't a night to get stuck on the pass. It ended up being closed for a couple days due to snow.