I'd vote for the Publix just next to the Premium Outlet Mall on Vineland Ave. The actual address is: Regency Village, 8145 Vineland Ave, Orlando, FL 32821. It's a pretty short detour off of I-4 at the LBV exit. If you come off the 535 exit ramp off I-4, turn left to go under I-4 (instead of turning right towards the entrance to DTD) then left at the first light at Vineland (Bahama Breeze is at this corner). If you follow Vineland around past the big church and the outlet mall, you'll come right alongside of Publix on your left. It is a very clean store and always a stop on on all our trips for food/Coke/beer. It has a great selection of Disney merchandise, as well, at "un-Disney" prices.

Try to avoid stopping on a Sunday morning due to church traffic, or Google the slightly longer but way less congested route skipping that first left and turning left instead onto World Center Drive (536) and then another left onto International Drive. The Publix shopping center will be on your left. There may be others, but that's probably the closest to WDW resorts coming from your direction.