You can definitely put some miles on your ATVs and find some great camping spots within 2 hours of Boise.
We like to camp outside Idaho City (highway 21) on busy weekends because the traffic isn't nearly as bad as highway 55. There are quite a few established campgrounds that take reservations and some areas that are dispersed if you don't mind dry camping. Most of the roads in the area allow ATVs including the main road through Idaho City.
Another nice place is the Tripod Meadows area near Smith's Ferry. There are several large meadows you can setup camp on and hundreds of miles of forest service roads to explore.
There are also several areas closer to town that you can go ride for the day. The Owyhee Front near Murphy south of Nampa has a mixture of trails and roads, most of which allow vehicles up to 50" wide. This area is mostly high desert terrain but longer trips take you up into the mountains and around some cool old mining areas.
Make sure you get PDFMaps on your phone and download the GPS enabled maps for the National Forests in the area. These can be a lifesaver on the twisty mountain forest service roads where it is very easy to get lost.
Here are a couple of links for you to check out:
http://www.stayontrails.com/where-to-ride/
http://www.riderplanet-usa.com/atv/trails/idaho_list.htm
http://www.riderdestinations.com/idaho-atv-trails/
http://trails.idaho.gov