Tokyo traffic is not the nightmare it used to be. In the last few years new cars are being registered at half the rate they were in the 1980's and early '90's as people keep their old one's longer and the youth have decided a trip to Hawaii is preferable to road tax. Indeed, crossing Tokyo during most times of the day is simple and quick and just requires a few dollars for highway toll fees.
That is except on a Saturday morning. Unusual characteristics come into play at this time. If it's a long weekend don't even try after 6.30am or before 12.00 noon. But if last week was a long weekend the roads will be more than likely clear as everyone wakes up remembering the nightmare of a few days before and decide to have a coffee and read the paper instead.
School holidays make a big difference. The final weekend before school starts can be horrendous whereas the first weekend after school starts can be a lonely affair. And then there's Golden Week in May and Obon in August. Only try to get out of Tokyo then if you really enjoy stationary traffic. But if you're OK with Japanese then you can help yourself a little. The Highway's Authority maintain an excellent real time website not only showing you current traffic but also forecast traffic for the next few days.
Enjoy your trip. Next article, the ever increasing tolls on Japan's highways...