It looks like you're new here. If you want to get involved, click one of these buttons!
Abode of Agony. You talk with a statue and she opens one of the gates: either yin or yang, depending on the gender of your character. You can't open both. Further inside, you need to have collected a special set of equipment.
Chu-chih Palace. The door in the Hall of Mirrors. You need a special Demon-Revealing Mirror you can buy in stores sometimes. Then, the switches need to be flipped down on one wall and up on the opposite wall.
The Temple of the Moon can be accessed from somewhere up the mountains and the Heavenly Palace is near the Temple of Ancients.