These chests are generally hard to find, since they are hidden in small places or behind walls.

Eregion - Search around the back of the Elven outpost, and there will be a small section of raised land behind the right wall. Go into it and find the chest.

Minas Tirith - Once you get to the highest level (the Citadel, where Gandalf tells you to find the Banner of Elendil), look behind a short wall that has some stairs near it. Open it and you will get a few very useful items.