Philip Seymour Hoffman left an unusual last wish for his young son — that the boy grow up in one of three artistic, cultural cities.

“It is my strong desire [that] my son, Cooper Hoffman, be raised and reside in or near the borough of Manhattan [or] Chicago, Illinois, or San Francisco, California,” the late actor said in his 13-page will filed in Manhattan Surrogate’s Court on Wednesday.

“The purpose of this request is so that my son will be exposed to the culture, arts and architecture that such cities offer,” the Broadway and Hollywood star wrote.

The Oscar-winning actor presumably meant the same for his two daughters, who weren’t born when his will was written.

The document was penned in 2004, almost 10 years before the drug-addled star died of an apparent heroin overdose.

Hoffman left the bulk of his fortune to his longtime girlfriend, Mimi O’Donnell, the mother of Cooper, now 10, and the couple’s daughters, Tallulah, 7, and Willa, 5.

He also named O’Donnell executor of his estate and trustee of at least one trust fund he set up for Cooper.

O’Donnell was made preliminary executor of Hoffman’s estate by a judge while the will winds its way through Manhattan Surrogate’s Court.

Court sources told The Post the family asked that his estate be handled on an expedited basis — a sign that the family needs cash.

O’Donnell and the children “rely on [Hoffman’s] assets for their support,” a lawyer for O’Donnell said in a court filing.

The grieving mom will now begin the grim task of sorting out Hoffman’s finances and clear his belongings from the apartment he’d been living in after O’Donnell reportedly kicked him out of their $4.2 million Jane Street pad.

In a court petition filed Wednesday, O’Donnell said she needs access to Hoffman’s accounts to pay for funeral costs, outstanding bills and the rent on the Bethune Street apartment where the actor was found dead by friends Feb. 2.

Hoffman’s net worth has been estimated at about $35 million by CelebrityNetWorth.com.

Hoffman stipulated in the document that Cooper’s trust should be used for the boy’s “education, support, health and maintenance.”

Cooper will get half the money in the trust when he turns 25, and the balance at 30, according to court papers.

It is unclear whether Hoffman subsequently set up trust funds for his daughters after they were born.

But his will contains language that will provide them a share of his estate under New York law, legal experts said.

O’Donnell’s court petition indicated that she doesn’t expect a challenge to the will, and probate is expected to be completed by June 18.