There are so many bars and Izakaya (Japanese pubs) specializing various categories. Exploring around Omoide Yokocho or Golden Gai in Shinjuku gives you a feeling of nostalgic Japan.
Most of Karaoke places are open until morning, so you can sing as much as you can!
- Darts & pool bar
Also tend to open till late. Bagus is one of the biggest chain in Tokyo. There are at least one branch in every major district.
- Manga Cafe
most of Manga Cafes are open until morning. Recently, there are not only manga but also newspapers or magazines. You will get a free refill of drink, there are internets and sometimes even a shower room! Even if you can't read Japanese, it might be a fun experience to spend a night at a manga cafe.
- Ramen at midnight
It is pretty common for a Japanese to eat ramen after drinking with colleagues. Some ramen shops are open until late, try having ramen after some drinks and feel like you are Japanese :)