There is nowhere to go and nothing to search. The 
Necronomicon is under the Astrologer’s bed, he is the one who finds it, and the only thing you do is raise his opinion of you to thirty.
That is worth saying plainly because the game tells you to find the book and then gives you a location that leads nowhere. Players spend hours sweeping basements for a quest that was never a fetch quest.
Four errands for the Astrologer are the whole route, ten reputation each. Do them and the book arrives on its own.
Why the quest sends you looking
The Donkey raises it once, in a quest called The Ingenious Gentleman Don Keyote. Agatha agrees to resume corpse deliveries, you go and tell him the strike is over, and you find him by the Graveyard.
The book comes up because it was his side of the bargain. He promised it in exchange for your help, and in the same breath he admits he cannot deliver.
The thing is… I don’t have it. / But I do know a guy who might know where it is. / It’s the Poet… now he’s an Astrologer… calls himself Gunter.
The Donkey, passing the debt along
That conversation is the last thing the Donkey has to say on the subject, and it is where the trail starts rather than ends. His icon stays on the quest in your log the whole way through, which sends people back to him for a next step he does not have.
Ask Gunter and he gives you something that sounds exactly like a destination. It is not one, and the game is being deliberate about that.
He said you know where the Necronomicon is. / Feh… yeah, it’s somewhere in my old stuff… from my former life. / Down in a basement.
The Astrologer, describing a place you will never visit
You then offer to fetch it yourself, and he turns you down. He is busy running the public relations campaign you hired him for, and he wants you to keep your side of that going first.
So… could you go down and find the book for me? / Look… I offered to help you, and I’m helping you. / If you want me to have time for your book, then I need you to help me help you.
The Astrologer, explaining the real mechanic
Nothing in the game places a Necronomicon anywhere in the world. It arrives in your bag from a conversation, so no amount of exploring the sewers, the tower or the crypts will produce it sooner.
The four errands that get it
Ten quests in the game award Astrologer reputation, ten points each, but only four come early enough to matter here. They run in a line, each one starting the next, and together they are worth forty.
First is the tarot cards. Speak to Linda to find out where the 
Deck of Cards is, then bring them to the tower. It pays ten reputation, a 
Town Gratitude and a 
Story.
Second is the sermon, where you preach once to try out the new Hypno-device. That one has no item cost at all and pays the same ten, so it is the cheapest rung on the ladder if you already have a church.
Third is the poetry book. Print a 
Printed Poetry at the press and carry it up to him, which pays ten reputation, another Town Gratitude and a Story II. Fourth is the signed agreement, where a 
Signed PR Agreement finishes the sequence.
Asking about the book needs twenty reputation and getting it needs thirty, so the first three errands are enough. The fourth is worth doing anyway, because the technology the book leads to is itself locked at forty.
Unlocking the conversation in the first place
Reputation on its own is not enough, because the Donkey only brings the subject up at the end of the Nun’s crossroads storyline. Three jobs come first: improve the graveyard and report back to Agatha, clear the blocked path, and fix the manhole at the crossroad.
Then you speak to Agatha to restore corpse delivery, which is the step that sends you to the Donkey. None of that has anything to do with a book, which is most of why the connection is so easy to miss.
With that conversation done and twenty reputation in hand, the first visit to the tower opens. Reaching thirty opens the second, and the second is the one that ends it.
What he says when you ask again
Go back to the tower at thirty reputation and the game pays off the joke it has been setting up since the first conversation. He never went to a basement either.
I already found it. / Turns out it was under my bed. / No wonder I’ve been having all those nightmares…
The Astrologer, on the great search
He hands it over along with another ten reputation and a Story II, and the achievement Forbidden Knowledge unlocks with the line that some books should stay buried. Asked whether it holds the ritual for resurrecting a zombie he says it does, with some commentary from the last Graveyard Keeper. Then he closes a sale.
By the way, if you need stones for the collars… I know a guy who can sell you some. / What guy? / Ha ha… it’s me!
The Astrologer, closing a sale
What the book is for
The Necronomicon is not a tool or an ingredient. Taking it reveals Reanimation Liquid, a technology that was hidden until that moment, which is the formula the voices in the resurrection room keep referring to.
Revealing it is not the same as affording it. The node costs thirty red, forty green and fifty blue, and it carries its own gate at forty Astrologer reputation, which is why the fourth errand is worth finishing even though the book only needed thirty.
Once it is bought, Reanimation Liquid is one 
Alcohol and one 
Catalyst for two, and it is what turns a corpse into a worker rather than a burial. The book is the gate to the back half of the zombie system, not a trophy.
Graveyard Keeper 2 Necronomicon FAQ
Where is the Necronomicon in Graveyard Keeper 2?
Under the Astrologer’s bed, and he is the one who finds it. There is no location to visit and nothing to pick up. Raise his reputation to thirty and ask him a second time, and he hands it over.
The Astrologer said it is in a basement. Which basement?
None. The line is a red herring the game pays off later, when he admits the book was under his bed the whole time. No basement in the game contains it.
How do I raise Astrologer reputation?
Four errands, ten points each. Bring him the Deck of Cards that Linda helps you find, preach one sermon to test the Hypno-device, print a Poetry Book and deliver it, and bring him the Signed PR Agreement. Three of the four get you to the thirty you need.
When does the Donkey talk about the book?
Once, at the end of The Ingenious Gentleman Don Keyote. Agatha agrees to resume corpse deliveries, you go to the Graveyard to tell the Donkey the strike is over, and he admits that the Necronomicon he promised you is not something he has. He points you at Gunter the Astrologer and never mentions it again.
Why does the quest point at the Donkey?
Because he starts the chain and the log keeps his icon on it throughout. Every step after that first conversation happens at the Astrologer’s tower, so going back to the Donkey achieves nothing.
What does the Necronomicon do?
Taking it reveals the Reanimation Liquid technology, which was hidden until that point. Revealing is not affording: the node costs thirty red, forty green and fifty blue and needs forty Astrologer reputation, which is why the fourth errand is worth finishing.
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