I've actually done this myself. It might not be the only way, but it worked for me (though you may have to deal with other things later depending on your mod). If you go to the
quest section, then load up
CG00. In the
Quest Stages edit entry 0.
Under the result script, add something to move your character. (ie, player.moveto xPlayerStartMarker ,or whatever you name an X marker). Then you might do things such as start your new quest (setstage alternateStartQuest00 0) or show an intro message explaining what is going on (showmessage alternateStartMsg).
Depending what you are doing, you will also likely need to tweak things. If it is still going to follow the story, only skip the intro (which there are likely mods for already (?) ), then you will want to make sure to go through the quests you are skipping. Some things, such as variables that would change depending what you did (ie, kill Atma's father or not) would need set.
If you merely wanted an alternative spot without story reasons, but just to start elsewhere, then the above should handle it. If you only wanted it for you and only as a different starting location, then simply rushing through the intro then using console commands would work to teleport you elsewhere, but I somehow doubt that is what you wanted... =)
If you are going for a completely new story, then you would have to take care of a great number of things. Is your person from a vault? If not, then all conversations where they mention it would need changed. Any quests calling you the vault dweller or speaking of your father would need a tweak. Any quests you don't want to be used would have to be disabled. For instance you might skip or heavily modify the homecoming quest (or whatever it was called) , as it returned you to the vault as a known person.
FINALLY (I think) if by chance you want the actual physical room to do some tinkering, that is located at Vault101d. Everything is hidden under black 'blocks', but if you find it easiest you can rotate the camera about them. The birth room is a small square room on the left side, about half way down (from the directly above view, default shortcut key T). If you still can't find it you can double-click something from the room in the list of items in the room; one example is CG00DadREF.
Hope that helps, and more questions just ask!