Almost every camp in the SI has at least one safe container. Find a camp you like, stick something memorable (like an iron arrow) in each container and leave the cell for at least three game days. When you come back, any containers that still have an arrow in them are safe. Of course everytime you are gone from the camp for three days, you will have to kill whoever is there, but I actually don't mind that. Also, some of the camps are quite neat and remind me of tree houses. I like them.
There are a couple places you can store stuff in New Sheoth, but I don't recall any specific ones off the top of my head.