Quick trip to Butte and Bozeman, Montana

Here are a few resources on Trippy:
Around Bozeman, the only recommendation I see is The Nova Cafe.
Near Butte, here are a few places recommended by a Trippy member.
For dinner and drinks, looks like Casagranda's Steakhouse & Guido's Bar is a good choice.
There might be easy hiking along the Milwaukee Trail, or you might be more interested in exploring Beaver Ponds Trailhead for better trails.

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.