Believe it or not, I visited both Publix locations on my recent trip. The one north of USF on Kirkman is only minutes away and probably the good choice if coming from the airport. It's in the NorthWest corner of where Kirkman meets Conroy road, a major intersection. Goto Universal like your normally would, head North on Kirkman, and you'll come to the intersection at Conroy. Make a left, and pull into the shopping center. The map shows it as being south of Conroy, but it's actually the Northwest corner.
So I went to SWF that day, then decided I wanted a Chicken Tender sub from the Publix Deli because they're so good. Yeah, that's right, I drove all the way from SWF to Publix for a sub. Went to the Sandlake location, and traffic wasn't bad. It's located on the South side of Sand Lake, about a mile west of I-4. Got my sub, ate half in the car, then drove to Tampa. Had the other half that night, because it's a cold sub, words can't describe how good it was.