Gonna be honest. I dont ever really run into jetlag issues. At a young age I was back and forth from San Francisco and New York on redeyes, so I've been naturally trained.
I'm heavy into mileage programs and credit cards with airline loyalty so my way of looking into flights won't help you at all since I have status. Also work takes care of a lot for me
Regarding Tokyo. Are you flying into Narita or Haneda? Haneda Airport is a easy subway ride into the city while Narita is a 45m Express train ride. In Tokyo make sure to hit the fish market early one day and try out all the seafood. Its mazing breh. Also, visit all the Team Lab interactive museum experiences. Youtube them. Districts... go to akihabara at night and see the arcades, anime shops and toy shops. Shinjuku at night is an experience, home to tokyos debauchery. Young people out all night partying, Tokyos apparent 'Red Light District'. Beware of the Nigerians trying to scam you into gogo bars. Shibuya more so for daytime shopping and a Japanese entertainment area. Roppongi for clubs and bars that westerners can enjoy. Ginza for higher end shopping and see ginza girls. Tokyo skytree and tokyo tower, you gotta go up to at least the top of one. Make sure to hit some temples. My fav 2 are Senso-Ji and Zojo-Ji. Make sure to eat some quality Wagyu Steaks.
You only need 1 full day in Kyoto. Osaka is even more of a foodie city than Tokyo. You defiantly have to experience their fish market. Honestly, I love going to arcades in tokyo and doing shyt i wouldve wanted to do as a teen. If you have a day go up to Nagano and go see the snow monkeys.