Tolls are expensive. Gasoline is equally expensive. Parking lot fees - yep, expensive. Street parking - illegal. Remember we drive on the left in Japan. In-car navigation systems are ALL in Japanese. Good, detailed, large-scale road maps are expensive to buy and again only in Japanese. English road maps are basic. National highways are numbered - the numbering is NOT often repeated on the side of the road - unlike for example France where there is a route marker practically every 200 meters. Streets in towns and cities are NOT named - hence the need for a navi system or large-scale Japanese map. I think you're asking a lot of yourself to enjoy driving for three weeks in Japan on what appears to be your first visit here.

I'd go for buses and trains. Cut your timetable down. Take the time to meet people when traveling - not an option in a car. People are generally friendly and courteous when traveling on a bus or train. On the road Japanese forget all their manners. They drive extremely recklessly and very little care or attention for other road-users.