In terms of Tsukiji, the big question is whether you want to get up at an ungodly hour to see the auction or you just want to see the market itself in action. You can probably tell by my description that I have not felt a strong need to see the auction.

The inner market otherwise opens for touring around 10AM. Admittedly, a lot of their day is done by then but you can still get a good flavor of the place. I would really recommend getting a guide to help you figure out what all is going on there. Otherwise, it can just seem a jumble of activity. I'm not going to list my favorite here but DM me if you'd like a recommendation.