I grabbed a screw driver and started removing hardware to get at the spaces behind the faux doors. The two under the stereo/TV area were plumbing access and a woofer. No luck there. However, under the sink is the air return grille for the furnace and, voila! A place to put the sink covers when the sink is being used.
That's the dish drying towel we set on the stove top showing up green.
As you can see, there is a bit of storage space in here. Just don't put anything in which will prevent the furnace from drawing air.