It is set in Los Angeles. I got to the end of the first episode, and you can clearly see the Santa Monica pier when she exits the vault.
I did a little reading, and apparently there are three interconnected vaults. It looks like each has its own exit to the surface, and their own dedicated connections to the other two. From what I gather they have nothing to do with one another except for once every few years they have arranged marriages in which they exchange members, to keep the family trees from turning into family vines.
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