For urban fishing locations, might I suggest Benkeibashi Boat Pier near Akasaka-Mitsuke Station? They offer pier or boat fishing with the cost of gear included in the entrance fee. There's also Ichigaya Fishing Centre near Ichigaya Station if you prefer a more catch-and-release style of fishing.
For saltwater fishing, there are plenty of charter companies operating out of Tokyo Bay. Can't go wrong with heading to Yokohama in Kanagawa Prefecture or Ohara in Chiba Prefecture either. Both are pretty accessible by train (or shrine-hopping). It'd also be remiss of me to not suggest heading to Okinawa. A further trip, but a truly beautiful area.
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For saltwater fishing, there are plenty of charter companies operating out of Tokyo Bay. Can't go wrong with heading to Yokohama in Kanagawa Prefecture or Ohara in Chiba Prefecture either. Both are pretty accessible by train (or shrine-hopping). It'd also be remiss of me to not suggest heading to Okinawa. A further trip, but a truly beautiful area.