There are three airlines offering flights to Tokyo. The most direct route isn’t necessarily the cheapest – being flexible is key to finding the lowest airfare rates. For example, try searching by month to see the best time of the week to fly. The cheapest date is currently 06 / Mar / 2019.
New Tokyo International Airport is just one of the airports in Tokyo. If you're not set on a specific airport, try changing your search from New Tokyo International Airport to Tokyo to see a broader range of flights – they might be cheaper. It usually takes about 27 hrs 40 mins to fly 9854 km to New Tokyo International Airport.
During this peak season, accommodation prices often increase too, so it's best to book early. Or you could keep your fingers crossed and hold out for a last-minute deal.