While Fallout 3 had 60 non-random stealth boys scattered around the wasteland, Fallout New Vegas only has 10. Their locations are:
Goodsprings: in the safe that's near the SW corner in the schoolhouse and in the inventory of Joe Cobb, who appears near the end of the "By a Campfire on the Trail" Goodsprings faction quest.
Lucky 38 Casino (New Vegas Strip): in a floor safe in the c0cktail lounge, which is only accessible after you talk to Mr. House.
Jack Rabbit Springs (SE of Primm): next to a skeleton and some ammo boxes on a hill in the center of the area.
REPCONN Test Site (west of Novac): on the floor next to a dead nightkin that's near the southern exit doors; in the safe in the locked room that's near the center of the middle floor (2); in the wall safe in the administrator's office on the top floor (2); on a table in the small dining area that's near the SW corner of the northern section of the basement
The Stealth Boy 3001 is a wrist-mounted device that generates a modulating field that transmits the reflected light from one side of an object to the other, making a person much harder to notice (but not completely invisible).
Find Fallout: New Vegas Game Guide & Walkthrough at GamesRadar.
Just In! Fallout fans may want to pay attention to QuakeCon later this month, as Bethesda has announced plans to host a Fallout 4 presentation at the event, led by none other than game director Todd Howard. Catch more at GameSpot.