If you are planning a trip by car, or considering whether to travel by car or some other form of transportation, the following site should help you calculate the relative costs in both time and money:
Unfortunately, it is only available in Japanese but I think it is set up in a way that makes it very accessible to people who are not fluent in Japanese. As an example, let's see how much we should expect to pay in tolls if we travel from Kumamoto to Kyoto.
First, we need to tell the calculator where we will get on the toll highway system. Since we will start in Kumamoto, we begin by clicking on the island of Kyushu on the map:
Then, click on Kumamoto:
And then the IC (interchange) you expect to begin on:
When you do this, you should see the following:
Click on the button on the left to set this as your departure IC. Then move the map image until you see your destination:
Again, click on the IC from which you expect to leave the toll road.
Then, click on the button on the right to confirm that you wish to travel to this point. Then, tell the calcultor whether you will be driving a K car (top choice), regular car (second choice), etc.
Now you are ready to hit "Search" . . .
. . . and find out how much you will pay and how long (at a minimum) your trip should take:
In this case, the tolls will cost you 11,950 yen and it should take you 9 hours 9 minutes to travel the 723.3 kilometers if you obey the speed limit and don't stop much.