Hi,
The nearest Walmart I know is when you leave Disney at Crossroads, turn left then right along I think it's called Turkey Lane road, which runs parallel to I4 towards Universal.
It's a quite new store and seems to stock most things you will need. We always have car, so not sure how much it would cost for Taxi.
Depending on where you are staying there are other supermarkets near to Disney. There is a good Publix on 192, which would be closer if you are staying Animal Kingdom or MGM area. Also a Goodings supermarket at Crossroads, near Downtown Disney, this is quite expensive and doesn't have a huge choice. Either way I think you will need some form af transport.
Hope this helps.