There is an Albertsons and a Super Target located at the intersection of Orange Blossom Trail and 417 just after you leave the airport area.
If you want something closer to WDW, you can go to the Winn-Dixie on Apopka-Vineland Road. Go past DTD on Hotel Plaza Blvd. Make a left on 535 (Apopka-Vineland Road) The W-D will be on your right about 1-2 miles.
To get to Publix, also near WDW, go past DTD on Hotel Plaza Blvd. Make a right onto 535 (Apopka Vineland Road), get into the left lane. Just after you pass under the I-4 bridge turn left and follow the road about 1-2 miles, you'll go past the premium outlets, Publx wil be on your left.