you don't indicate how you are getting to the Port Orleans resort, but no matter, there isn't a grocery within walking distance anyway.
If you're arriving on the Magical Express bus, you'll have to rent a cab at the resort after you check in to get to the grocery store.
If you're taking a taxi or towncar from the airport, you can ask them to make a grocery stop for you on the way.
The grocery I would recommend is the Winn-Dixie on Apooka-Vineland Road.
It is a short ride from the Downtown Disney/Marketplace area. Their prices are reasonable and the store is well stocked with anything you might need.
In addition, if you are so inclined, there is an ABC liquor store in the same plaza.
One final suggestion for you... I have stayed in the moderate resorts before, and find the refrigerators to have less than adequate cooling. I always pick up an inexpensive styrofoam cooler for the room. Just take it to the ice machine and fill it every morning. The ice will easily last the entire day. depending on the food you plan on keeping cold - I also take a box of ziploc plastic bags in my luggage - that way I can store everything & anything in them. They're also great for putting a washcloth in to take with you to the parks.
Hope this helps - have a great trip