Unless you really like sleazy bars, I would recommend Shinjuku over Roppongi - it's far less sleazy and there aren't touts everywhere that you have to avoid. It's only about 7 minutes farther on the subway (the same Oedo line) than Roppongi. Shibuya also has an all-night scene with a younger crowd than Shinjuku or Roppongi, and it's also easy to reach via public transit.
Besides clubs and bars, there's Don Quixote (with branches in all three neighborhoods) - a weird all-night variety store - and a late-night pingpong club and bowling alley in Shibuya if you're in a sporty mood.