The grocery store in Cross (roads) near the Pizza Uno is not Publix, if you're talking about the chopping center near Downtown Disney--it is Goodings, and is very expensive. There is a Publix south of Crossroads, just under the I-4 overpass, take a leftonto Vineland and go around 1-1.5 miles to Publix. There is also a Winn-Dixie north on Apopka Vineland Road, about 1.5-2 miles from the intersection of Apopka and Hotel Plaza Blvd.
The most convenient to me is the Albertsons on Orange Blossom Trail off of 417 coming from the airport to WDW. Exit and go straight across Orange Blossom into the parking lot. If you turn right onto Orange Blossom, there is a SuperTarget on the right just past the overpass.