Hi, Kimberly! You would have to be up for a pretty good walk to hit a convenience store, as there aren't any terribly close by. You will find quite a few things in the way of snacks at the resort, both at the food court and in the shop on property.
Another option might be to have some things delivered. Check out
www.gardengrocer.com . I've used them a couple of times, and they can have your items delivered directly to your resort. They run specials and take coupons!
There are a couple of gas stations with convenience stores on Walt Disney World property, but they aren't terribly easy walks. You can take a bus to Downtown Disney, and there is one across the road. If you have way more energy than I ever do, you can walk down Hotel Plaza Boulevard to the Crossroads shopping center. You'll find a Goodings Supermarket there, but it is quite a haul to walk the distance from Pop Century!
You might also consider taking a taxi to one of the stores. Especially if it's warm, and depending on the types of snacks you are buying, it might be best not to have to worry about walking back with a sack of groceries.
Have an absolutely magical vacation!