I have no idea what port you are going to or when, but I am headed down to port canaveral right now and will be looking for a Walmart/target type store. I can let you know if your not leaving any time soon.
For Port Canaveral, two exits west of the port (exit 49) there is a Publix grocery store, a Walgreen and liquor store if you head south on 3. About a mile.
On the main street that runs from Port Canaveral towards Cocoa Beach, there are a few Publix, a Walgreens, a CVS, and a Liquor store. My husband bought our beer and wine at the grocery.
One thing you can do since you have time is go to google maps and make a map of the port area - there's a target, and you can put in publix, Walmart and other places and have it plot them in the map - I made a custom map showing the port, our hotel, Ron Jon and other places we wanted to stop before getting on the ship....
We used to stay on Cocoa Beach pre cruises. There's many hotels and there is a Publix supermarket. We would pick up waters, etc there. Publix is a nice supermarket, and very clean.
There are also many nice places to eat and they even have a Dunkin Donuts.
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