The wireless is probalby only "visible" to those close enough to the common areas that support it. I always bring a small travel router (about the size of a deck of cards) to convert wired access to wireless, and enjoy the convenience.
I don't know which Pubix is closest---probably the one up by HGVC. I tend to go to the Winn Dixie just north of hotel plaza blvd off (I think) Palm Parkway. It's a few minutes past goodings, but still quite close, and easy to get to from that corner of WDW.