how do I go to Yokohama?

Hi, could you advise me on how to get to Yokohama from Shinjuku? By Shinkatsen? Could I buy the ticket on the same day that I am going? Thank you.

It is easier, faster and cheaper to take the direct Shonan-Shinjuku Line (unless you are heading to the Shin-Yokohama Station area).

If you need to take the shinkansen, take the Yamanote Line to Shinagawa and then the shinkansen for just one station to Shin-Yokohama. I recommend to buy a ticket for an unreserved seat, as it is considerably cheaper than a ticket for a reserved seat. You can buy the ticket at Shinjuku on the day.

As mentioned you can take the Shonan Shinjuku line direct from Shinjuku Station to Yokohama Station (where you can make connections to other trains that will take you deeper to where you need to go in Yokohama).

No real reason to take the Shinkansen.

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If you want to do it on the cheap, take JR train to Shibuya and change to the Tokyu Toyoko Line to Yokohama.
This requires a slightly long transfer, but it costs 410 yen vs 540 yen direct from Shinjuku Station. But because tourists rarely get off at YOKOHAMA Station it might be better to stay on JR trains, and changing at Yokohama to say Sakuragicho station or Kannai Stations where the tourists sites are at in Yokohama.