Originally Posted by
banzani
You could also take the regular train to Shinagawa and change there to Shinjuku. I recommend to check the schedule but would be optimistic it is still running at that time. Fun, efficient, cheap.
I don't think I'd necessarily recommend this because you'd want a second taxi at Shinjuku so it is getting complex. But if you do, the last Yamanote line train from Shinagawa to Shinjuku is at 12:47am, so it doesn't really add much, if any, slack.