Shinjuku handles more people than any station on earth, something over three million a day, and the thing most visitors need to know about it is that none of them are catching a Shinkansen. There are no bullet trains here. If you are staying in Shinjuku and heading to Kyoto, your journey starts with a local train to Tokyo or Shinagawa.

What Shinjuku does have is almost everything else.
Two options, both easy.
To Tokyo Station: the Chuo line rapid, about fifteen minutes, for the Tokaido line west or any of the northern lines.
To Shinagawa: the Yamanote line, about twenty minutes, for the Tokaido line only. Shinagawa is the easier station to navigate and is often the better choice from Shinjuku.
Both are covered by a Japan Rail Pass. Allow half an hour on top of your Shinkansen departure time and you will be comfortable.
This is the useful one. The Fuji Excursion limited express runs direct from Shinjuku to Kawaguchiko, the lakeside town under the mountain, in a little under two hours. A rail pass covers the JR section as far as Otsuki; the private Fujikyu line beyond that is extra. Seats are reserved and sell out in good weather, so book ahead. Alternatively the highway bus from Busta Shinjuku does the same trip and is often cheaper.
The pass covers the Narita Express, the Chuo, Yamanote and Shonan-Shinjuku lines, and the JR part of the Fuji Excursion. It does not cover the Odakyu Romancecar to Hakone, the Keio line, the subway or the highway buses.
Shinjuku has more than two hundred exits and people genuinely do get lost for half an hour. The simple version:
Pick your exit before you go through the gates. Crossing between them underground with luggage is slow.
Too much to list. Omoide Yokocho, the alley of tiny yakitori bars beside the west exit, is the atmospheric choice. The basement food halls of Isetan and Takashimaya are the best places in the area to put together something for a train. Ekiben are sold on the Narita Express platforms.
If you are booking individual journeys rather than using a pass, these are the routes that start here.
And the longer route guides, with times, seat tips and what to see when you arrive:
Historical accident. The Tokaido line was built to terminate at Tokyo Station in 1964 and the northern lines followed it there. A Shinjuku extension has been discussed for decades and never built.
Yamanote line to Shinagawa, then the Keikyu line, about forty minutes all up. Or the Limousine Bus from the hotels and Busta Shinjuku, which is slower but door to door.
For eating, nightlife and day trips west, yes, one of the best. For Shinkansen departures it adds a connection, which matters less than people think.

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