Tokyo has an excellent public transit system so you'd be fine in either place. I don't know the exact location, but guess that the Shiodome hotel will be closer to the JR station, although the Shinjuku Hilton has a regular free shuttle bus to and from Shinjuku station (every 20 minutes throughout the day, and every 10 minutes during peak times).

Shiodome is closer to Tokyo station if you're taking shinkansen rides. However, the new Shonan Shinjuku line pretty much makes Shinjuku station to Yokohama about as fast as Tokyo station to Yokohama -- also Kamakura.