The zombie reference is metaphorical. He's afraid that he'll become a "zombie" in life.
The verses (and a lot of the album) describes these really mundane, everyday rituals of family life and moving on into middle age. The narrator is just going with the flow: doing what is expected of him, not disappointing anyone, reading the script of his movie, keeping his shitty thoughts to himself and only telling his wife about them after she's asleep. It's making him turn into a "zombie" though... he's becoming less enthused about life, he's unable to express himself, going through the motions, becoming a "confident liar," etc.
In the last verse he states all of the anti-zombie things he wants: to be romantic, to believe, to be safe, to continue loving his wife... but he's ultimately afraid he'll "eat her brains". He's afraid that the ritual of everyday life will strip him of his appealing aspects until he's unable to feel emotion (like a zombie) and cause him to do harm to the person he loves and wants the most (eat her brains).
It's a man commentating on the effects that his marriage and middle age are having on him. This could almost be ‘Slipping Husband' from the husband's perspective.
The chorus confuses me though. It sounds as if he may be making reference to other men in his position - ‘We'll leave the silver city'. The ‘silver city' could be interpreted as the "perfect" lifestyle that the narrator's tired of.
Berninger, as always, is extremely self-deprecating although this song unusually contains some justification for his self-pity.
The symbolism of a ‘silver girl' may be reference to his wife and thus, the wives of all men suffering from the dysfunction he describes. The fact that Berninger uses the colour silver may be homage to the bitter feelings he has towards the stereotype of a trophy wife.
He acknowledges his flaws; ‘I'll try to be more romantic' but ultimately blames this dysfunction on the trophy wives who aspire to mediocrity.
Toward the end of the song, the repetition of the line ‘I was afraid I'd eat your brains cos I'm evil' suggests he left his spouse, returning to a self-deprecating persona because of guilt.
I think use of "silver cities" and "silver girls" symbolises the ideal trophy wife and the links this has with an upwardly mobile capitalist dream, with the "silver city" a representative of wealth and power, very similar to the "silvery citibank lights" in Mistaken For Strangers, which seems to portray the same sort of disillusionment with the upwardly mobile corporate lifestyle. This lifestyle seems to place many constraints on the person portrayed in the song, as they keep their "shitty thoughts" to themselves and doesn't tell his wife how he is truly feeling. He also seems to feel guilty for this as he tries not to upset his friends by revealing these toxic sentiments which make him "evil", as he cannot believe in the lifestyle in the same way the others can. There are zombie references and this could relate to mass consumerism and its effect on society, but in this respect it is flipped; instead the person disillusioned with this way of living is the zombie as they fester infectious thoughts through their corrupted "black dreams" of American corporate life.