From Roppongi Hills walk to Roppongi, Metro to Kayabacho, Metro to Takebashi, then walk to Kōkyo. 41 min ¥426. From Roppongi Hills taxi to Kōkyo. 7 min ¥3362. From Roppongi Hills Uber to Kōkyo. 7 min ¥4133. From Roppongi Hills walk to Kōkyo. 1 h 4 min.
There is no direct connection from Roppongi Hills to Kōkyo. However, you can take the walk to Roppongi, take the Metro to Kayabacho, take the Metro to Takebashi, then take the walk to Kōkyo. Alternatively, you can travel from Roppongi Hills to Kōkyo in around 7 min.