Aiiro is the best place to start any night out in Shinjuku-nichōme, thanks to the all-you-can-drink beer for ¥1000 happy-hour special from 6pm to 9pm daily. The bar itself is teeny-tiny; the action happens on the street corner outside, which swells to block-party proportions when the weather is nice. There's a red torii (gate) out front; you can't miss it.
Aiiro is welcoming to all and staff speak excellent English. This is a great place to find out about other events and happenings in Ni-chōme.