Adachi fish market is a genuine place of trade specialising in wholesale seafood. But from mid-2016 the market has opened its doors to the common folk on the second Saturday of every other month. Yes, it’s not that often and, yes, it’s only for two hours, but if you’re looking for a more local experience than the Tsukiji Fish Market tour then this might just be the answer. There is also a few restaurants selling great food at reasonable prices (open until 1pm).
See here for a post on Adachi Market with photographs and a list of upcoming market dates.