Belgrade probably is not the most spectacular town in Montana, but hey, it's still Montana. I grew up just south of there near Livingston, and it's been a while since I have been in Belgrade. I do know it has exploded with development so most of the farm land around the town is probably no longer. You may be able to walk somewhere to get a good view of the Bridger Mountains, but they are not to impressive from Belgrade. They are on the other side though!!
If you can get a car, take this tour. From Belgrade, make your way to Highway 86 and head off to Wilsall. Then take Highway 89 South into and through Clyde Park and go into Livingston. If you have some time, Highway 89 goes south into Paradise Valley and will eventually land you at the entrance to Yellowstone. If you don't then I-90 will take you back to Belgrade. On this route you will see a little bit of all landscape types. When in Wilsall the mountain range to the east of the town although on the map it is called Lewis and Clark National Forest, the locals call it the Crazy Mountains. They are beautiful. This would be a very good early morning to evening drive that would allow for a fair amount of stopping time!!
Hope you enjoy your trip and let us know how it goes.