There is a Publix on 192 but every time we try to use this road (we usually go during the summer months) it takes forever to get anywhere. Even with the construction done, this road moves very slowly a lot of the time.
The new Publix, which is near HIFS, is actually on SR535. HIFS is on SR536. Take a right out of HIFS on 536, opposite direction as the DisneyWorld gate, and take this road until the first major intersection with a stoplight which is 535. On the corner is a small shopping mall. Take a left on 535 and follow this past the Holiday Inn Sunspree, under I4, past Crossroads shopping mall and the Goodings supermarket, and then about 1 1/2 miles on your right you'll see the new Publix set back off the road.
SR535 also gets busy, but we still like it better than 192.