Shibashi is one of the older train stations in Tokyo. Is a mayor commutation hub that can get really crowded at rush hours. But walking along the bridge, surrounded by the smell of Ramen noodles or Yakitori, and having a beer or two in a small Izakaya is one of those experiences that allows you to catch a glimpse of the real flavor of Tokyo.
Tsujiki is much more than the Fish market. There are lots of interesting spots worth the visit around here. Specially after sunset
Personally, I would not recommend visiting any fish market in the morning unless you are really into fish, but somehow getting up early and visiting Tukiji's fish market in the morning is some sort of a trend among tourists. For me is better to walk around there when things are a little bit more calm and you get to enjoy walking around Tokyo's most popular fish market.