What train station do I use?
 

I'm staying at the Westin in Ebisu. Should I travel from Shinagawa or the main Tokyo train station when going to Nagoya, Kamakura and other places?

Shinagawa is definitely closer to you for Shinkansen and Tokaido/Yokosuka (for Kamakura). But I'm not sure all Shinkansen stop in Shinagawa, so watch out.

They've changed the schedule so that lots of shinkansen stop at Shinagawa now, although not every train. But it looks like at least 2/3 of all trains do, so it's pretty convenient. When you arrive at Narita, stop at the JR tourist office and get a copy of the English language shinkansen/limited express schedule, it's free.

Of course, if you are going north or west from Tokyo, you'll have to go to Tokyo station, although taking an express Saikyo line train from Ebisu to Omiya is another attractive option since virtually all Shinkansen going north or west stop there as well.

Edited to add:
There is also rapid service from Ebisu to/from Yokohama, where you can change trains to go to Kamakura. I believe a very few of these trains actually go through to Kamakura, but most likely you'll have to transfer. When I was in Tokyo last week, there were signs on the trains noting that the frequency of the Shinjuku-Yokohama (and points north and south) route was increasing on October 14.

One train an hour goes directly from Ebisu to Kamakura (although as RichardinSF said the frquency will increase next week). If the train is bound for Zushi or Odawara it will stop at Kamakura. It takes fifty minutes.

If the train is bound for Zushi or Odawara it will stop at Kamakura. It takes fifty minutes.[/QUOTE]

Does that train go to Hon Atsugi?

No. Hon-Atsugi is on the private Odakyu line (departures from Shinjuku via Shimo Kitazawa).

If Disneyland...
 

This may not apply to you, but if anyone is staying in Ebisu and wants to go to Disneyland, you can skip the incredibly long walk thru the bowels of Tokyo Station to the Keiyo line...

From Ebisu you simply take the Saikyo line toward Omiya which then becomes the new Rinkai line. Take this all the way to Shin-Kiba and you are just one or two stops to Maihama/Disneyland on the JR Keiyo line. Its probably a bit more expensive since you go JR to Rinkai to JR, but well worth the reduced wear and tear on your feet (you will get enough of that at Disney!). :)