Gallatin peak is the highest mountain in the Spanish Peaks and is visable from all over the Gallatin Valley. While many backcountry skiers have long visited Gallatin Peak in winter to ski it's many couloirs, mostly located on the north face, it also makes an invigorating summer day climb. If you want a more liesurly pace, there are many lakes and streams that offer great camp spots and it is certainly a nice place to spend a few days.
You might run into Goats, like I did near the top.
There are several accesses to Gallatin Peak, all of them are a bit of a hike. All accesses are via Gallatin Canyon. You can go in up the South Fork of Spanish Creek from the Spanish Creek Trailhead: Turn right just after you enter the canyon, cross Ted Turner's ranch, follow the signs. Or you can go in by the Indian Ridge trail, across from Squaw Creek a little further up the canyon. Or Hell Roarin' yet a bit further on. I think the quickest way is from the North Fork trailhead, located a couple miles past Lone Mountain Guest Ranch, past Meadow Village at Big Sky. There is a good trail (#16) about 6 miles up into Bear Basin. At the head of Bear Basin you turn right (East) on trail #189 up over the Bear Basin/Hell Roarin' divide. You can follow the trail to Hell Roarin' Crk, then climb back up to the base of the mountain, or you can find your way down before decending all the way to the creek.
No red tape. By the way, this peak is suitable for Dogs via the easiest route (South Face)
Duh, camp anywhere. If it's a real dry summer there may be fire regulations in effect. You are in the Lee Metcalf Wilderness area, so wilderness regs apply (don't bring your chain saw).