Domestic flights in Japan do not take an important part of transportation as like the United States or island nation such as Indonesia.
Normally the main mean of transportation within Honshu island is by trains. Thanks to bullet train; Shinkansen most of the big cities in Honshu are connected with Tokyo by Shinkansen.
Cities which have more than 1 million inhabitants but not connected by Shinkansen is just Sapporo which is located in Hokkaido. Kawasaki also does not have Shinkansen station but Kawasaki station is just 18 minutes away from Tokyo station. Even cities more than half a million have Shinkansen station except Matsuyama which is in Shinkoku and cities which are in Tokyo Metropolitan Area.
If the train journey is more than 4 hours, people prefer to travel by airplanes. Therefore the major way to travel between cities in Honshu and Sapporo or cities Kyushu are by airplane. Of course, the way to travel to Okinawa is by airplane.
Then, convenient and fastest way to travel to the minor islands and travel within Hokkaido are by airplanes. Most of these airports in minor islands do not have direct flights from Tokyo. However, if you are traveling from Tokyo, better to buy the air tickets together with a single airline to enjoy the discount. For example, if you are flying to Tanegashima island, only Japan Air Commuter which is a subsidiary of JAL has daily flights to the island from Kagoshima airport. Therefore if you buy a flight ticket between Tokyo or Osaka to Kagoshima, better to fly by JAL rather than ANA or other airlines to get the discount for Kagoshima-Tanegashima.
On the other hand, there are airports which have only ANA flights. In this case, you should fly by ANA from Tokyo or Osaka.