To the SuperWalmart - turn left out of WH, then left onto the 192. Travel about 10 mins to US27, at the end of the 192. Turn right onto the 27 and SuperWalmart is almost immediately on your right at Cagan Crossings.
Winn Dixie (only good for basics IMHO!) - left out of WH, left onto 192, it's a few minutes along on the left, in Formosa Gardens plaza, look for Taco Bell, Giordanos Pizza and Carabbas.
Which Publix did you try? I'm looking forward to trying the new one at the bottom of Old Lake Wilson so I'd be interested in hearing about it if it was that one!