The Bridger Range is located north of Bozeman, Montana. It's a north to south oriented range and known for its steep limestone slabs rising straight out of the ground on the eastern flank of the higher peaks. The link above takes you to a fantastic page about this range.
The Madison Range is located southwest of Bozeman and is another north to south oriented range with a handful of peaks breaking 11,000 feet in elevation. This is a beautiful area to find some solitude as fewer people venture into this more remote part of the state. The Madison River flows north in the large valley just west of the range and empties into the Missouri River. Huge mountains flanked by steep Limestone cliffs are common here.
The Crazy Mountains are another north-south oriented range located about 50 miles east of the Bridger Range. Heading east on I-90 from Bozeman you can look north near Livingston and see these peaks. Crazy Peak is the highest peak here and offers some good steep snow climbing routes and ski descents.
This small mountain range is located just northwest of the Madison Range and are the ones you see as you drive east on I-90 after crossing Homestake Pass just east of the city of Butte. At 10,604 feet, Hollowtop Mountain is the highest point here, but the hiking is superb throughout the range. The origin of the name "Tobacco Root" isn't well known but the natives in the area may have grown tobacco in the valleys surrounding the range.