Locker

Locker
 

I always thought it was casillero but is cajón a better word for a locker where you can store clothing or a coat, or is there a better word than cajon?

I wouldn't use cajón, unless it's said in a particular region.

Both casillero and locker are common.

I agree with Rusty. You can't hang anything inside a "cajón". Those are for storing folded clothes.
I think a piece of furniture where you can store clothing like a small wardrobe at the entrance of a house, would be a "ropero", "armario" or "guardarropa". Maybe "clóset" if it were embedded in the wall.