If you haven't been in Japan in twenty years, then it might be worth taking the monorail to Hamamatsucho and back -- I always get a "ooh, I'm in Tokyo again!" kick out of it, especially if you snag one of the limited expresses that makes almost no stops along the way.

But I'm also drawing a blank for anything interesting else to do in the area in the early morning. If you had a bit more time and arrived a bit later, the gardens of Hama-rikyu Teien are not too far from Hamamatsucho, but they open at 9 AM so they're not really an option for you.