Originally Posted by RichardInSF
Although Roppongi is fairly close to Shibuya (maybe 20-25 minute walk), there isn't really a direct connection via subway that I am aware of.
Correct. Your best bets are either Hibiya Line to Ebisu (one stop) and transfer to JR Yamanote to Shibuya (one stop); or walk just a bit north of Roppongi to Nogizaka, then take Chiyoda Line to Omote-sando or Yoyogi-koen and walk a bit south to get back to Shibuya central (a map would be advisable for this though...).