In Goodsprings, between the Saloon and the General Store are 4 XXX crates. You can move and stack these next to the bench's. They are safe to store items in.
As you travel; ammo, first aid, and tool boxes are always safe. In a pinch, the nuke-cola machines are also safe.
Later, once you arrive at the Lucky 38, turn left when you first enter and under the stairwell is an area with a multitude of lockers and safes. All are safe to store items and with so many you can organize them as you like.
Note: Do not use the other containers in this area; suitcase, cash registers, etc. These are not confirmed safe.
In the world, lockers (other than those mentioned above), file cabinets, metal boxes, garbage cans, and most garbage dumpsters are never safe.