Grocery stores are bad for zombie outbreaks, too many weak walls and entrances. Plus, it's too big and you could have several zombies pouring in without knowing until you're totally surrounded.
I would go to a school, actually.
Food from the Teacher's Lounge and cafeteria, Entertainment from movies they keep to play on free days, Medical supplies from nurse's office, Weapons like a bat from Gym, Terrain is good, because it's standard for schools to have few entrances and brick walls with hard to get down doors, no vehicles.
Also shelves would get knocked down FAST by zombies.