One can be found in the Goodsprings schoolhouse, in a locked safe (Lockpick 25).
Another is carried by Joe Cobb.
Several can be found at the REPCONN test site.
One can be found inside, next to the dead nightkin near the front door.
Another can be found in the basement, on one of the tables in the room with the sign reading "Food".
Veteran Atticus in the Caesar's Legion safehouse can give two to the player for free, each time they encounters him there during his visits.
The repeatable side-quest Caesar's Favor can provide a random supply of Stealth Boys each time, sometimes in very large quantities ( of up to 95). A high reputation (liked or idolized) with Caesar's Legion may be required.
One can be found in the middle of Jack Rabbit Springs, beside a skeleton found lying near an upright post visible on the hillside.
Approaching the cattle pen at Brooks Tumbleweed Ranch reveals a nightkin who offers to sell you a 'wind brahmin' (a tumbleweed) for all your caps. The nightkin carries a Stealth Boy in his inventory.
One can be found in the REPCONN Headquarters behind a locked door (Lockpick 50) in a container on the top floor.
With the add-on Old World Blues, passing the "Robot Compliance Test" to upgrade the stealth suit Mk II at the X-13 Research Facility will yield a Stealth Boy in the reward safe. This test and three others can be repeated and give random rewards each time, including Stealth Boys.
In the nightstalker test area of the X-13 Research Facility, shooting the forcefield in the ceiling of the small room with the Strange Still with an upgraded sonic emitter will drop a Stealth Boy into the room.
Stealth Boys may randomly spawn in ammunition boxes.
Many can be found in the footlockers at Camp Golf