So, after playing through the DLC and, due to many deaths, having to reload and go through several conversations multiple times I believe I have heard of every bit of Elijah's dialogue. Near the end, he explains that the reason he wanted into the vault is for the hologram technology and for the vending machines so he could use them to build his own society. That fits with the character, and I'm fine with that. What I don't understand is why he would want into the vault at all. There are no holograms inside the vault proper, though there are several in the basemant itself. However, there are more holograms littered about the casino itself, and even quite a few within the villa. The vending machines are found in the villa and casino as well, but I don't believe there were any in the vault/basemant. One could argue that he knew the gold was down there, but I don't see the reason in that. The vending machines don't take gold, they take chips, and there were no chips in the vault/basemant I'm aware of. Even if there were, there's thousands of chips in the villa and casino. You could say he wanted to use the gold to trade for caps or something else he wished to use for currency, but he doesn't seem one to be interested in creating an economy. He wants obedience. With the hologram technology he could kill anyone who disobeys and they would be helpless to defend himself.
I don't understand would dedicate all this time (years maybe?) to breaking into a place that houses absolutely nothing that he claims to want. Even if he did not know what was inside it, why would he put so much effort to get in when he could take all things he wanted without even entering the casino itself. He built a holorifle, I don't think it would be too difficult for him to replicate more vending machines or holograms once he had one in his possession to understand how they work.
On a side note: Any ideas how the vending machines are supposed to work exactly? They obviously hold more items then they would normally be able, and I imagine even if they did hold them all that they would eventually run out. I don't see how they could change the chips into the items either. Plastic and food are entirely different things.