From Tennoji you can catch the Haruka train directly to Kyoto. While the total travel time is similar to most of the standard routes that Hyperdia suggests, taking the Osaka loop line to Osaka then connecting to Kyoto, you save yourself a transfer. From Kyoto Station, you can pick up a 500Y day bus pass and for unlimited travel around Kyoto. I much prefer the buses compared to the subway. And if you are heading to Fushimi Inari or Arashiyama, it's an easy transfer at Kyoto Station.