General terms:
* Harem: This is the most direct synonym, referring to the women's quarters in a palace, especially in Ottoman times.
* Palace chambers: This emphasizes the location within a palace.
* Private apartments: This highlights the private nature of the rooms.
* Women's quarters: This focuses on the occupants of the rooms.
More specific terms:
* Gynaeceum: This term from ancient Greece refers to the women's quarters of a household, which could be considered an ancestor of the seraglio.
* Courtyard: This could be used if the specific chambers were located within a courtyard.
* Pavilions: This could apply if the chambers were separate buildings within the palace grounds.
Ultimately, the best substitute depends on the specific context and what aspect you want to emphasize.