The Shinjuku Ramen Jiro is my second pick (after Ikebukero) for a Ramen Jiro that is a good choice for a first timer. It's also consistent and tasty enough that I find myself here every couple months or so when I am in the area. The line is rarely longer than 15-20 mins long.
The Shinjuku Ramen Jiro has an expanded menu, including different sizes of tsukemen, good for hot summers. The noodles here are fairly firm by default, and they are a bit thicker than average Ramen Jiro noodles. Yasai are mostly moyashi. The broth is relatively fat-free compared to other Jiros, which enhances its strong shoyu taste. I can also taste a bit of pepper in it but maybe that's just me. The pork is not the rough fatty cuts you see in most other Jiros but rather relatively thin slices, not too different in size and shape from what you might see at a yakiniku place. The store is a little cramped but it also has two tables, each seating two people. It appears to be OK to wait for the two tables if you want. The staff are friendly and quick. Feel free to grab some manga from the shelf near the ticket machine if you want something to read while you wait.
Don't get this Ramen Jiro confused with the one on the other side of the Yamanote-sen in Kabukicho (歌舞伎町).
ramentokyo.com Ramen Jiro Information Page