You have several options!
Take the south exit of the airport to the 417.
1. Get off at the Orange Blossom Trail exit at the end of the exit there will be a SuperTarget to your right on OBT.
2. If you make a LEFT onto OBT, there will be a PUBLIX on the right side about 3/4 mile up the road in a plaza.
3. From the 417 you could get off at the John Young Parkway exit. Head south on John Young and you will see the Hunters Creek Plaza PUBLIX on the right side.
4. If you continued down John Young heading south you will come up on the Loop. Although not any grocery stores in The Loop, there are restaurants, stores like Ross, JCPenney,Kirklands,Michaels,Yankee Candle, etc.
Just past the Loop if you make a right on Osceola Parkway, there is a PUBLIX on the left side.
Then you would just follow Osceola Parkway the rest of the way to Disney.
5. If you get off at exit 6 on the 417, make a right onto International Drive. Turn left onto Vineland and there will be a PUBLIX in that plaza on the right side.
6. If SuperWalmart is your go to place for groceries. There are a couple options for these.
One is off of CR535 and Polynesian Isle-the other is on Palm Parkway (which changes names to Turkey Lake Rd) SuperWalmart will be on your left side.
Have a great trip!