When out with the fam (car camping) we always take the turnoff to the Iron Creek Trailhead (west of town?). Along the dirt road are a plethora of good campsites with water access from Iron Creek. It's typically quiet and is easy access to any of the main start-off points in the Sawtooth Mountains. Also to note is there are existing firepits in these camp areas, and you generally do not need to even bring firewood. I've been simply walking across the dirt road to the slash piles and taking what I want. Doing this for the past 2 years with no issues.
Good luck with your hike... maybe we'll see ya on the trails!