Seriously, the two areas I'd pick to emphasize would be the Asakusa/Ueno area (Sensoji Temple, Ueno Park with National Museum) and the Shibuya/Meiji Shrine/Harajuku area. The first would give you older Tokyo, and the second would give you trendy Tokyo, with time out for a quiet stroll through the Meiji Shrine grounds.

This keeps you in two areas of the city instead of zigzagging back and forth.

If it's a clear day, you might want to squeeze in an elevator ride to the top of a tall building. If nothing else, you'll see just how vast this megalopolis is.