Honestly, Terence, I'd like to respectfully suggest that you not try walking to anywhere off property from SSR to buy groceries. The walk itself might not be so bad, but folks are so busy sightseeing on those busy highways, you might end up a hood ornament, plus you've got to haul all your purchases back to your villa.
You can get basics right there at Artist's Palatte (although the prices put you in mind of the Tower of Terror, just as high - but you ARE on vacation, and it IS Disney), or, maybe, the Hess station across from DD. Dunno what cab fare would be to Publix/Winn-Dixie/Wal-Mart, especially if they had to wait on you.
We like Winn-Dixie, just because the prices are good, and it's easier to get in and out of than Wally World. But we typically have a car, too.