Resting

Resting is used to heal in a safe place without the need to use Stimpaks or healing skills.

Fallout and Fallout 2
In Fallout and Fallout 2, you can rest in any place, as long as you're not in combat, using the Pip-Boy 2000 alarm clock function.

Fallout 3
Beds are used to heal completely by sleeping. You can not sleep in an owned bed, but if the owner dies the bed usually reverts to an unowned state. Many raider camps have beds that can be used after killing the raiders.

Free Locations

 * Arefu, In the last house, named the West Residence.
 * Inside the Jury Street Metro Station, initially guarded by 3 raiders.
 * At the Super Duper Mart, in the ladies room & near the pharmacy, initially guarded by 2 groups of raiders (one roaming, one local). Also expect some action when you fast travel to the location, just run inside if you are too damaged and sleep first.
 * With The Family in the Meresti Metro Station, upstairs. Watch out for the mines on the way in.
 * Just south of Dukov's Place, in the little raider camp. Initially guarded by 2 raiders. Some strong but stupid Mutants nearby. To defeat the Mutants: Try to lure one to you, watch out for his firepower, hide behind a pillar, use a Shishkebab to set him on fire, and eat away his health. If he tries to shoot at you, hide again, behind your pillar.
 * The houses in the Minefield can be unlocked and contain many beds inside, you may want to get rid of any mines and the sniper first though.

Hotels

 * Megaton, Moriarty's Saloon, Nova, 120 caps.
 * Rivet City, The Wheaterly Hotel, 120 caps.