The quest should tell you which world/area to look in. Once there, look on your map. The quest arrow won't show up but the chest will be on your map. Also, FYI, don't assume you have to battle the enemies in the room. In several areas you can just walk right around them and open the chest. Good luck!
If you don't remember where specific places are, you can use Google (include the word "wizard101" in the search) to find them or you can use the search function on the Wizard101 Central forums.
Correct as long as you have done all quests, you will see the Chests like all Bosses beaten on your map... There are some Chests that you dont have to battle to GET, but some you must beat the Boss again to claim the Chest....Good luck