I go to the Xindian Carrefour often. It's near the printshop that I do business with, so I've gone there for lunch in the food court as well as to buy food and gifts to take back to the U.S. That Carrefour might meet most of your daily food needs, although I have no idea what specifics you require, and I would expect the Tianmu and Neihu locations to be stocked with similar items. All are on the outskirts of Taipei city proper; a long trip might not be worthwhile considering how plentiful food markets are throughout Taipei. Depending on where you will be staying, consider other supermarket chains like Wellcome.