Bozeman is the home of the
Museum of the Rockies and
Montana State University:
https://www.museumoftherockies.org/It has an extensive collection of dinosaur and other paleontology collections.
However since you mentioned you love hiking and the outdoors, you will only be 90 minutes from
Yellowstone National Park. If one of your half days is an afternoon, go for it. You will not regret it. Take the route straight south from Bozeman through
Big Sky into
West Yellowstone. From there it is a straight shot into the park and
Old Faithful. You can drive around the park for as long as you like, but if your time is limited, drive the Geyser Plain as it is quite spectacular. If you plan to eat dinner before you head back to Bozeman, there is a wonderful fine dining room near the North Entrance which has amazing food. Elk run freely on the grounds of the Park Headquarters. You can go out the North Entrance through the Roosevelt Arch into
Gardiner and back to Bozeman.
