Personally, I think Publix has a pretty good wine selection. And one thing I love that we don't get up here is that they have buy-one-get-one-free on a regular basis. Last time we were there, we picked up two really nice Australian wines that were BOGO.
Like you, we'll usually just have the taxi wait while we run in a get a bottle of wine to have during the cruise and a bottle of champagne to open when the cruise begins. Plus, we'll usually get a couple of bottles of water and a 12-pack of soda. We refill the bottles from the water supply on the ship as their water is usually pretty good. If it's not, then we'll just buy a few more bottles in port, which is always much cheaper than buying it on the ship.