Late night local chat
This area is great for meeting people who are either taking a break before leaving for home, after arriving, or after missing their last train.
In Shinjuku, these areas are right outside the Kabukicho exit, in front of Alta (with the large TV monitor overhead) next to the fruit shop, and outside the west exit.
In Shibuya, Hachiko is the most famous meeting area.
Right next to it, there is a smoking area, and another newer smoking area closer to the koban outside the station exit.
If they are waiting for a friend you could either try to get their contact information for another day, or alternatively, try to befriend the friend when they arrive and join the party for a drink!
Whether their night was a success (drinking with their friends) or a feat of endurance (watching the clock until the boss stops drowning them in shochu and forcing them to listen to rude jokes), the transition to the last train usually has people in a good mood.
If she’s enjoying herself in your company (it doesn’t really take that much), she might voluntarily miss her last train or agree to come for “Just one drink.” If it’s after last train time (ish), then most people are out for good.
If a woman is by herself, there’s a decent chance she missed her train and now has no plans – perfect opportunity to make a new friend who might just end up becoming more!
Then, when they approach simply smile and demurely mention you’ve missed your last train.
If you’re a guy – it won’t be as easy, but the existence of such nanpa-shi illustrate that it’s neither strange nor culturally insensitive to talk to strangers on the street – in fact, it is very much a part of Japanese culture.