Pine Creek campground (406/222-1892, www.fs.fed.us/r1/gallatin [1], Memorial Day–Labor Day, $11) is 10 miles south of Livingston [2], then six miles east of Highway 89 up Pine Creek Road (reservations at 877/444-6777, www.recreation.gov [3]). Pine Creek Falls is a short hike from the campground, and Jewell and Pine Creek Lakes are three miles up the trail.
Sites may also be reserved at Snowbank (406/222-1892, www.fs.fed.us/r1/gallatin [1], Memorial Day–Labor Day, $11), 20 miles south of Livingston on Highway 89, then another 15 miles east on Mill Creek Road.
Closer to Gardiner [4] and Yellowstone National Park, Tom Miner/Petrified Forest Forest Service campground (406/848-7375, www.fs.fed.us/r1/gallatin [1], June–Oct., $7) is eight miles west of Highway 89 on Tom Miner Road (36 miles south of Livingston). The Gallatin Petrified Forest is a two-mile hike from the campground.
The many fishing-access sites on the Yellowstone River [5] are also de facto campgrounds.
The Forest Service has cabins for rent up Trail Creek, 20 miles southwest of Livingston [2], and Big Creek, 28 miles south of town, then eight miles west on Big Creek Road. These cabins are rented year-round for $30 per night; winter visitors may need skis or a snowmobile to reach them.
Contact the Livingston ranger station (406/222-1892) for reservations.
Links:
[1] http://www.fs.fed.us/r1/gallatin
[2] http://www.moon.com/destinations/montana/the-missouri-headwaters-and-south-central-montana/livingston-and-the-paradise-valley/livingston
[3] http://www.recreation.gov
[4] http://www.moon.com/destinations/montana/the-missouri-headwaters-and-south-central-montana/livingston-and-the-paradise-valley/gardiner
[5] http://www.moon.com/destinations/montana/the-missouri-headwaters-and-south-central-montana/livingston-and-the-paradise-valley/paradis/sights