'grocery store' in Italian

I'm planning a trip to Rome, Naples, and the surroundings and I'd like to locate a few grocery stores in these city centers to put on my Google maps. I tried 'grocery store', which didn't work so well, and 'Negozio di Alimentari' which gave me two sorts of results: shops with words like 'tropical', 'zoo', and 'animali' in the name, and also several results with the word 'di' in the name but not 'negozio' or 'alimentari'.

If y'all could please provide me with a better phrase to search for, or even just some common grocery store chain names in Rome and Naples, I would be grateful! Thanks!