There's also peer-to-peer car rental, where private owners list their vehicles directly. Rates tend to be lower than traditional agencies and the selection is more varied since you're picking from what locals actually drive. You can browse car rental options in Tokyo here:
https://getrentacar.com/en-US/japan/tokyo . Owners set their own terms so pickup and drop-off arrangements tend to be more flexible than what you'd get at a standard rental desk.