In any big city, you definitely have to be proactive.
Whether NY or Tokyo, the truth is there are just so many people, you have to stand out to get noticed and have people come to you.
If that's something you're not good at, then you need to place yourself in situations where you're slightly vulnerable; just enough for someone to take interest.
In this sense, joining a gym, international circles, taking up a new hobby (shogi, go, calligraphy, tea, flower arrangement, etc) can be extremely rewarding.
Not only do you gain intellectually, culturally, and physically, but by opening yourself up to new experiences and people, and you invite people to help you, reach out to you.
As for cafes
The SegaFredo in Shibuya is a great place for people watching and meeting people. http://www.segafredo.jp/storelocator.html#p1
But in general, if you take some long walks through Shibuya, Omotesando, and Shinjuku, you will find some great cafes.
Hey, it only takes a smile to start up a conversation.