Nothing in the game is missable, but I recommend starting working on treasure chests from the very beginning.
The Watchplains (9 Treasures)
Entrance area - near the Gate, right side.
Steps ahead from the entrance, left area, in a dead end.
Hidden behind the big rock on the way.
Backroad 2 - go straight after entering and take the right path during the crossroad.
Backroad 2 - Behind wooden hut, just before entering the next area.
Backroad 3 - there's a hidden passage by the left.
Backroad 3 - Near the save point, hug the wall to your left.
Backroad 3 - After defeating the boss, this chest is near the watchtower, by the left of the stairs.
Secret Backroad - Don't take the gate after defeating the boss, instead, take the left side stairs to reach the secret area, the chest is behind the Black Chocobo.
Note: you can now complete the sidequest in Cornelia Town by speaking with the knight near the fountain.