^The trains run late on the 31st, because hundreds of thousands of Japanese are going to shrines to say their new year's prayers (called Hatsumode). I left the arena at 1am, was stuck in the crowds for at least 90 minutes, possibly 120 minutes, then caught the Yamanote line back to Ikebukuro. I didn't get to my hotel until nearly 4am. I've tried to block that part of the night out because it was pretty awful.
So my advice is, if you go to the 31st show, leave when the final song starts, or even before, so you're not stuck in sardine like conditions for 2 hours. Seriously, you'll be so squished against random people, its uncomfortable and embarrassing.
