Hire a private tour guide for a four-hour or so walking tour that's customized to your interests. The hotel should be able to recommend a few tour guides and it's a great way to get to know a city.
A few places you should go regardless include the fish market, the Tokyo Tower (the orange Eiffel Tower looking structure), and Akihabara (Electric City).
Also see
What’s Doing In Tokyo for a few more suggestions.