I think that Tsukiji fish market is the most famous market in Japan among tourists from abroad.
Today, I'd just like to introduce another market in Tokyo.
That is Farmer's market.
The market is open from 10AM, so you don't have to get up so early like 4AM lol.
It is closed at 4PM. And it is held every weekend in front of United Nations University (thew nearest stations are Shibuya station and Omotesandou station).
You can communicate with farmer there. They know a lot about vegetables and fruits and we can get serving ideas from them.