I just mapped it, and the Publix at 7880 Winter Garden Vineland Rd, Windermere, FL 34786 looks like the closest to BRV, per Google maps. Winn-Dixie might be a little closer, but you’d have to deal with more congestion getting there. Sometimes we choose our Publix based on ease of getting there rather than distance or travel time!
we like the Publix on 535, just below I-4. They have great precooked meals that just need to be reheated, saving you time by not cooking. There is also a Walmart supercenter right up the road that is also easy to get to.