By default people seem to think they should fly into Tokyo, but arguably for the most common sites, basing yourself in Osaka is quite useful, with easy day trips to Nara, Kyoto, Hiroshima and Kobe easily doable on the shinkansen. And often it’s cheaper to fly in to than Tokyo(!).
The airlines are ususally Hainan (5-star long haul) to China, then a short hop with the low cost carrier Spring Airlines, and sometimes (the cheapest) with Sichuan Airlines.
