"If my guardian cannot reside in any of these cities, then it is my strong desire, and not direction, that my son, Cooper Hoffman, visit these cities at least twice per year throughout such guardianship," he wrote.
Hoffman explained that he wants his child to be exposed to the culture, arts and architecture those three cities offer.
The contents of the late actor's will were revealed on Wednesday. It was written almost 10 years ago. He has since had two more children with his longtime girlfriend, costume designer Marianne "Mimi" O'Donnell. He did not update his last testament after his daughters were born.
Hoffman left much of his estate to O'Donnell, with a trust fund for their son, now nearly 11. Papers filed with the will value Hoffman's estate simply at "$500,000-plus."
The Oscar-winning actor was found dead Feb. 2 in his Manhattan apartment of an apparent heroin overdose. The 46-year-old star of "Capote" and "The Master" said in interviews last year that he had sought treatment for a heroin problem after 23 years of sobriety.
The Associated Press and ABC News contributed to this report.