Other than supermarkets people buy groceries from

depa-chika- department store basements which generally have a huge mix of fresh and prepared foods. If you turn up just before closing and can fight the oba-Chan then you can be rewarded with some heavily discounted sashimi

independent stores - lots of butchers, grocers, fishmongers, tofu shops etc. around. Butchers especially are great for a good value bento at lunch time.

antenna stores - do you miss the taste of your home prefecture (or are searching for a sake or and ingredient you can’t find anywhere else) then they prefecture themed stores bring a selection of regional specialities to Tokyo