I'm a fan of spending the night before or after a long flight in the city of Narita, but even I think four nights would be excessive.
Once you've been to the temple and the shopping center, there isn't a whole lot to do.
If you're interested in contemporary Japanese culture, Tokyo is the place to be.
Since you're relatively young and interested in the culture, I'd suggest buying the Rough Guide to Japan and planning your itinerary from there. The questions you're asking suggest that you haven't done that yet. You have two months, so get yourself to a bookstore and start reading.