Anywhere in Whiterun or Riverwood?

Silent Moon Camp is a area that has a chest. A group of bandits live in the immediate area, but after you kill them you can put your stuff in their chest with no fears. My brother had his loot in there for a week or so. Its in the plains near whiterun

There is one place with DB.

Dragonreach. Put 'em in a barrel or desk, it'l be safe.

According to the in-game help on containers, ONLY if you OWN the container. It clearly says that if you stash stuff in a container that is not owned by your character don't expect that it will be in the container when you return. If do and lose your Vorpal Great-sword of Doom when it or the container goes poof, you can cry all the rivers that you want, but the GM's, Mods, Devs, and all the rest of us don't really want to hear about the problem.

Now if you want to just make a quick post along the lines of "Hey, the chests in Such-and-such Dungeon go poof or empty out after X number of In-game days" then that is a different thing all together.

I used a Container that is in Dragonsreach that is to the right a ways away from the entrance of Dragonsreach.. It was close to a table. Forgot what it was.

I've used it throughout the game so it's safe. Test it out if you'd like.