The limousine bus is the most direct way to get from point A to point B. But you've got seven hours between flights. Assuming it takes you a half-hour to clear formalities and you want to be at Haneda an hour or whatever ahead, that gives you some time to muck around. I'm inclined to tell you to take your stuff on the Narita Express into Tokyo (or Shinagawa), put your stuff in a coin locker there (700 JPY for a big one), and then go take a walk.

Tokyo station is near the Imperial Palace, which is generally closed to the public with the exception of the East Garden (which is closed Mondays and Fridays). You're also near the Tokyo National Museum of Modern Art (also closed Mondays, 420 JPY). I can't offer you any personal recommendations for eats there. Research something, or maybe stumble upon something.

To Haneda: Take the Yamanote or Keihin-Tohoku line to Hamamatsucho and transfer to the Tokyo Monorail OR take aforementioned trains to Shinagawa and hop the Keikyu Airport Line OR take a limousine bus from Tokyo Station (departs every 30-60 minutes). The train options are the faster ones.