Fairy Lake - Free, 1hr from downtown
Battle Ridge - $10, 30 min from downtown
Hyalite - either $30 or free, 30 min from downtown (ask me)
Bozeman is a 2-hour drive from both the North and the West entrances to Yellowstone National park.
Fun fact, if you show up before or after the hours of gate operation, you can enter without paying
If you’re looking for outdoor activities, some easier hikes to do with close proximity to town are the M trail or Drinking Horse. One highly rated hike is Lava Lake (moderate), on the way to Big Sky. Just don’t forget the bear spray (this CANNOT be flown with)