Crammed one on top of the other, the little local places serving everyone's favorite grilled meat on a stick will make you feel like you've stepped out of modern Tokyo and into some mythical parallel dimension of exactly what people who have never been here expect Japan to be. Friendly staff, don't expect any service whatsoever in English. Take the Japanese friend assigned to you upon processing through customs and have them help you order.
On the west side of Shinjuku, this little area reminded me of a district in ichijoji which has the same 'days gone by' feeling to it. This tiny narrow street and side streets is full of good places to find cheap beer and greasy or salty meat, most often pork or chicken. Only the adventurous would come here on a date, but it is a good place to go as a small group. Too many people, and you won't all fit in a single bar.
Tall people watch out though, there are some very low corrugated roofs to cut your head on.