I too would recommend leaving the airport.
I would look into staying in Shinagawa... it is very easy to get there to/from HND. There's not much to see/do in Shinagawa. But if you choose to go sample some nightlife, you could easily do a short train ride to Shibuya or Ebisu and then take the taxi back to the hotel. Plus there will be some places open late into the night in Shinagawa. Even if you're primarily just going to sleep, the garden at the Prince Grand Takanawa / Sakura Towers / New Prince Takanawa complex is very pleasant and it'll be nice to get out of the airport as jib says.