The Monforton schools are part of Gallatin County, not Bozeman city schools. The schools here are very well regarded. Their boundaries are approximately Love lane to the east, Durston to the north, River road to the west and Upper rainbow to the south. It covers Four corners, part of Gallatin Gateway and then over to Black Bull. Walkable neighborhoods include Black Bull and Middle Creek Parklands.
For a full review, check out this report by greatschools.org.