I grocery shop at Publix, but used to go to Wal-Mart for things like diapers, laundry detergent, etc. No need for that at all now with the Pier Park Target. The Target in Destin is a few miles west of the Wal-mart, but I'd still suggest going to Target instead of Wal-Mart. If you're at Seaside or east, the Pier Park Target will be closer (and much faster drive) than the Destin Wal-mart. Also, Targets have a small food section where you can pick up a gallon of milk, loaf of bread, etc. so you don't have to make two trips.
Another thing to consider about Wal-Mart--you must take a cooler(s) for the refrigerated items and the ice cream will probably melt before you get it home. It is much more convenient to shop at Publix where you can be home in 10 minutes instead of 45!