First some markers. 192 is the road that runs east and west through Kissimmee. 536 is the main road that comes off the interstate (I-4) as exit 26B and runs right by OKW and goes by Epcot. 535 is the road that goes from The Crossroads (where a Goodings is and right near the Disney Village Hotels) then 535 crosses 536 and joins up with 192 on the east side of I-4. World Drive is the Main Entrance to MK and comes directly off of 192 near I-4 going right by Boardwalk. Buena Vista Drive is the road that goes from Downtown Disney to MGM (passing BW, etc area) and on to Animal Kingdom & Coronado Springs. Finally Bonnet Creek Parkway is the road that goes beside OKW passing Port Orleans and Dixie Landing. Whew!!!
Super
WalMart and Publix #1 (corner 536 & 192).
From OKW, you can get there by going out of the resort and turning left on Community Dr, then left on Bonnet Creek (at the light) to Buena Vista Drive (2nd light I think). Turn right and go under Epcot Center Drive (536) and take the entrance ramp going East toward Kissimmee. On 536, go about 2 or 3 miles to the first major intersection (first light also i think) and take a right on 535. Go about 2 miles and 535 will dead end into 192. Publix #1 is one your left. If you turn left onto 192, Super Walmart is on your right about 1-2 miles or so.
From BW, leave the entrance and turn right on Epcot Resort Blvd. Turn right on Buena Vista Drive and then go sourth (away from the parks and toward 192) on World Drive. When you get to 192, go East and follow 192 about 4-5 miles and you will see Publix on the left where 536 joins with 192. Continueing on 192, Super Walmart is a mile or two more on your right. NOTE: THERE ARE DEFINITELY A COUPLE OF PUBLIX CLOSER THAN Walmart.
Publix # 2 (West of I-4 on 192)
From OKW, you can get there by going out of the resort and turning left on Community Dr, then left on Bonnet Creek (at the light) then right on Buena Vista Drive (2nd light I think). Continue on Buena Vista Drive past MGM and the Epcot/Swan area then turn left, sourth (away from the parks and toward 192) on World Drive. When you get to 192, go right and it's about 3 or 4 miles on the right. It's essentially out of town so you'll think you've missed it.
An alternative from OKW would be turning left on Community Dr, then left on Bonnet Creek (at the light) to Buena Vista Drive (2nd light I think). Turn right and go under Epcot Center Drive (536) and take the entrance ramp going East toward Kissimmee. Take I-4 West and then exit on 192 going west and it's about 3 or 4 miles on the right. It's essentially out of town so you'll think you've missed it. This way is longer but likely easier unless I-4 is backed up.
From BW, leave the entrance and turn right on Epcot Resort Blvd. Turn right on Buena Vista Drive and then go sourth (away from the parks and toward 192) on World Drive. When you get to 192, go right and it's about 3 or 4 miles on the right. It's essentially out of town so you'll think you've missed it.
Besides the Goodings at Crossroads, there is also one on 192 West of World Drive (it's on the south side of 192).
I seem to recall someone mentioning a new Publix store on 192 between I-4 and the Publix #1 above but I don't see it on their locator site at
http://www.publix.com/ap_store_locator.htm. I believe the one on West 192 is the easiest and quickest if staying at BW, either Publix is about the same from OKW though I believe the one at 535 and 192 might be slightly easier to get to because of less traffic lights. There are several other Publix including one just south of Sea World, a couple actually in Kissimmee and one on 417 East of WDW. Maybe someone else knows where other stores are that might be helpful for you.