Grocery Options

Moving this also to the Disney Camping forum.

When I search, I'm finding two that are 13-14 miles away; both in Kissimmee - one on International Drive. Hopefully, someone who knows the surrounding area more closely will be along soon....

Shopped for groceries while there last month. The closest is about 15 minutes away.
Take Osceola Parkway west as if you were going to Animal Kingdom. Just before the AKL make a left on Sherberth Rd. to US 192. Make a right about 2 miles. WD on the right Publix on the left.

You asked about Publix, and I agree with Pox24 about the closest Publix. If you are interested, there is also a Wal-Mart Supercenter also off International Drive and also within about 15 minutes of FW. Either are good options, IMHO.

When I lived there, and even when I visit, I find the one past Lake Bryan to be the most convenient. That would be about 7 miles from Fort Wilderness. It's also convenient if you're planning on visiting DTD (Springs, yes, I know, lol) for dinner or such when your first get there, which we typically do.

You just go out the gate that is near DTD (Buena Vista Dr.)
Turn right on 535
Take a left at the first light (Vineland Ave) after you go under the i4 overpass
Then just follow the road around a couple curves until you see Publix on your left

There are also a WalMart Supercenter and a Publix on SR 535 (Apopka Vineland Road). From Disney Springs (See ? I got it right!) take Hotel Plaza Boulevard to 535 and turn right. WalMart will be 3 miles on your right. Or continue down 535, which dead ends at US192; Publix is in the shopping center to your left at that intersection. And if you're really adventurous and want to try Target, make a left onto 192 and a Target Superstore will be on your left about a mile from 535.