So I am considering writing a FoE fic but I wanted to make sure I didn't steal any vaults that may have been used by other authors. Since I don't have the time or the energy to read every single fic in the universe (or read every single "canon" fic), I thought I might ask and see if we can make a list here to see which vaults have been taken.

All the vaults are listed here. I chose 68 and 50 for Shaping Shadow. The side fiction ones are, at times, doubled up. These are user submitted. I know many people do not post their stories on the wiki. I have mine posted and keep it updated as I keep adding new chapters. It is a great way to keep track of things yourself and help your readers.

http://falloutequestria.wikia.com/wiki/List_of_Stables

6401603 This helps somewhat... it is a shame that a lot of the numbers I had in mind were already taken.

6401615
Thankfully, these are not cannon. I know, we all want originality, but we can use the same ones. You can see the doubles. You also could use letters and numbers, words and other things. The ones at the very bottom have some cool techniques to make it yours.

If your intention is to make your FoE story work with all of the side stories, it wont. It can't. They already contradict each other. Thus is the nature of these things.

6401595
Well, the good news is, Fallout: Equestria only names eight stables (Mindrop's link is good for details on those). Those are the only "canon" stables, but there's nothing wrong with checking the list to pick your own number.

Incidentally, that wiki is pretty good as a research aid. It's not 100% accurate, but it can usually get you the information you need.

Edit: and what he said. You pretty much can't avoid contradicting some other side-story. I wouldn't worry too much about it.

I have Stable 16 in my fic "Influx" with Stable 34 being mentioned.

My other fic "Broken Steel" has Stables 22, 88 and 112 as explorable Stables.

We use Stable 76! However, that being said, as long as the number isn't used in the canonical stories of Fallout Equestria, you are completely allowed to use any number you wish!