Kitchen (and bathroom) cabinets usually have what is called a "toe-kick" - the area between the floor and the bottom of the cabinet. The toe-kick is most often recessed - and guess what? There's nothing there but space waiting to be used.
You can do this in a rented apartment as long as you are careful - take your time, and you'll end up with an awesome stash spot.
Best of all, this doesn't cost more than a buck!
Here's what you need to get started:
Putty knife with a thin blade
Some sort of pry tool, putty knife with thicker blade or flat piece of metal
A trim tool - used to pry molding from base boards
Diagonal cutters or tin snips
Hammer or mallet
File and sandpaper
Block of wood to protect the surface you're going to hammer
Vacuum cleaner or broom (optional)
4 rare earth magnets
Four screws or nails with heads - make sure they're attracted to magnets
Small piece of thin plywood (optional)
Box or other container to fit the spot (optional)
Step 1: Identify the spot
The baseboard needs to be a separate piece of wood, i.e., not attached to the cabinet itself. Most floor cabinets are set up this way.