Check in first, then go shopping. To get to Publix, go the same way as you would go to Goodings, but hang a right on SR 535 & follow to Hwy 192 (about 7 miles). The plaza with Publix will be on the left just prior to Hwy 192. You will also pass a Super Wal-Mart on the right if you go to this Publix.
The Winn-Dixie on SR 535 is one of the nicer Winn Dixie's, and is a lot closer than Publix (about 4 miles from the Fort, verses 9-10 miles to go to Publix.)
As a Floridian, I prefer to shop at Publix, but when you are on vacation, time is of the essence. The Winn-Dixie would be your better choice. PLUS, there's an ice cream shop in the same plaza as W.D. and a Walgreen's across the street!!!
If you wish to dine off property, there is an Olive Garden on the SE Corner of SR 535 & Palm Pkwy, a Ci-Ci's Pizza Buffet one block east of SR 535 on Palm Pkwy, a Hooters about 1 block further down from Ci-Ci's, and (my fav) a Miller's Ale House on the NW corner of SR 535 & Palm Pkwy. The Ale House is a sports bar, but they have a really nice dining area & terrific menu with reasonable prices. There are many more restaurants in this area, but I've only named the ones I've eaten at.
ENJOY!!!