There are 3 Walmarts that I know of and have been to, numerous times, around the Kissimmee/Orlando area. There are lots more that I have NOT been to, but I will focus on these 3; they are the ones my GPS and hotel staff have directed us to as being the closest. These three all are supercenters (i.e., large grocery departments with fresh produce and meats, as well as frozen (and canned, too) and they all are open 24/7. The two Walmarts that are not on 27 also have decent-sized Disney souvenir departments.
One is on Rte. 27 just north of 192 (aka Irlo Bronson Mem'l. Hwy.). Being the furthest away from DW means that this store will be less crowded. Officially, it is in Clermont, FL. If you're driving west on 192 from I-4 or the FL-Tpk., you'll pass several different sites of all the usual chain restaurants as well as a Target SuperCenter too.
TIP: if you want to eat at any of those chain restaurants, it might be worth the short drive further from the I-4 area, for the lower crowd levels and better service - IMHO.
If you don't want to go that far, there're the other 2 that we use, first the one that is known as the Calypso Cay
Walmart, due to its proximity to Calypso Cay Resort, at 3250 Vineland Road (aka Rte. 535), just north from 192, past the LBV Outlet Mall and Calypso Cay Resort. It's actually the closest one to AKL.
What's really nice, to me, anyway, being from Philadelphia, PA, is that right next to the Walmart is one of the new Wawa stores! The best coffee, hoagies, and steak sandwiches from Philadelphia

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And the last WM I will be referring to is down on 192 (east from I-4; a bit over 7 miles according to the WM website).
If you must go during the peak Disney seasons, and you don't want to stand in long lines at the cashiers, then go to the one on 27. We have been to the other ones almost exclusively, and we often visit during Christmas week, and the lines are ginormous. Next time we're there that week, we'll be making the extra effort

to go to Clermont lol! Some things just have to be learned the hard way

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Hth.