I was able to pull the following pics from the site, Chara Hiroba which posts which plushies will be available for the next upcoming weeks/months in the various machines across Japan. Now I just need to work on my Claw Machine skills and get a plane ticket to Japan :P
There is a Mobile App Game , Facebook Fan Page and Twitter page though they are all in Japanese. This page under the drawings (click on the dark blue Japanese writing link!) offers free wallpaper downloads of NemuNeko. If that isn't enough, you can also waste time checking out the cute Nemuneko pics on tumblr.