Lived in Bozeman for 5 years, was GM at Boodles and Gallatin Gateway Inn
Stay away from Louie's, the Mint, and JB's Bistro - low quality/high price
Also avoid Santa Fe Reds, Main St Overeasy & The Bay, no matter what anyone says
Cateye Cafe & Soby's for breakfast
McKenzie River for decent pizza
Plonk for wine and snacks
La Parilla for cheap burritos
The Crystal for whisky and lots of it
Not much to recommend in the way of 'fine' dining
You might try conducting some searches, but here are a few...
John Bozeman's Bistro, Gallatin Gateway Inn (outside of Bozeman), Plonk, McKenzie River Pizza, Louie's Down Under, Pickle Barrel, Boodles, the Mint (in Belgrade). Some of my info may be slightly out of date, but that'll give you a start.