The Hostel is a great place to stay: cheap, everything needed is provided, supermarkets and a bento shop are right beside it. Power sockets for different plug types are provided. The check-in is very easy and convenient and communication is super fast!
If you want to explore Shinjuku and its nightlife, you can easily go there by foot. I even walked to the metropolitain Government Building (great and free observation platform) and from there on to the Meiji Shrine, Harajuku and Shibuya and took the metro just on the way back.
The mattress is very japanese, that means, very hard and thin. Nevertheless, I slept wonderful on it.