1. Treasure chest in Lowtown, outside of Old Dalan's place
2. When sneaking into the palace (Before getting the Goddess Tear), there are several chests in the Cellar. Do not open the two chests in the southeast corner.
3. All treasure chests in the Confiscatory (the place where you get your weapons and armor back after being captured)
4. In the Phon Coast, later in the game, there is an island with 16 chests all near each other. The 4th chest that must NOT be opened is among these, so it is best to leave them all alone. They only contain Gil anyway.

If you've left all these treasures be, you'll find the Zodiac Spear in the Necrohol of Nabudis. It sports a whopping +150 attack and, like all spears, +8 Evasion.