Just so you know, Haneda has free wireless under network TIAT. Rabbi Edery's sushi is great, his chef actually picked me up from the airport in April and he is well trained, picks out the fish himself and everything. Tsukiji is fantastic but you're getting in a little too late to catch any of the real action. Still get to see more fish than you ever have in your life though.
Narita is a solid hour from anywhere you would need to go (Narita Express is a rip off, stick with the Keisei Skyliner, faster and better).
From Haneda everything is 30-45 minutes. If you're going to Akihabara (which is really worthwhile especially if you like electronics/or are a gamer) you're better off taking the Monorail to Hamamatsucho and transferring to the Yamanote (bright green) or Keihin Tohoku (blue).
If you're going towards Shibuya you're going to want to take the Keikyu Line towards Shinagawa and transfer there to the Yamanote. Shibuya Crossing is an unbelievable sight, tens of thousands of people crossing a street every few minutes, youtube it, the Starbucks on the 2nd floor across from the station is a good place to watch. Also, right near Shibuya is Harajuku, the hip fashion district where you'll see some pretty wacky get-ups. On the main street out of Harajuku station is a 100 yen shop (equivalent of a dollar store) called Daiso with some really quirky and cheap Japanese goods.
Meiji Jingu Shrine and Asakusa Temple are pretty impressive but theres an avodah zarah concern. My Rabbi said as long as you go in with a big tourist group it shouldn't be an issue as nobody would think you're going in there to actually pray.
If you're a history buff, it is well worth it to check out Yasukuni Shrine and especially the museum attached to it. It is run by Japanese nationalists and gives a revisionist history of Japan's militarism from the 18th century onwards. Lots of cool relics from WWII, planes, kamikaze fighters, cannons, etc.
Whatever you do, don't take the train from the airport! Rabbi Edery can tell you some funny stories about guys running into his house with cab drivers chasing after them with the bill!