As mentioned, the Shinkansen is operated by JR Tokai and not JR East. If you wish to use a pass that is specifically for JR East trains, you can use the slower JR trains. Assuming your nearest station is Tokyo Station, the following is a typical route.Tokyo Stn. - Yokohama Stn.
JR Tokaido Line
Yokohama Stn. - Higashikanagawa Stn.
JR Keihin-tohoku Line
Higashikanagawa Stn. - Shin-yokohama Stn.
JR Yokohama Line
This trip takes about 45 minutes.
On a related note, however, as much as I would like you to visit Ramen Museum, my favorite museum in my neighborhood, I'm not sure if it's worth the trip. You might want to visit other spots in Yokohama while you're at it. If you're interested in soccer, the Nissan Stadium near the museum has guided tours, but the touristical spots are located more towards Yokohama Stn. or Sakuragi-cho Stn. both accessible by JR East trains.
