I am looking for the best (and cheapest) method of transport from Yokohama Port to the Tokyo Intercontinental Hotel. We will be dragging lots of luggage!!!!

Just a joke. I would suggest a taxi from the boat to Sakuragi-cho or Yokohama station. Then take JR Keihin-Tohoku line to Tokyo station, then taxi from there to hotel. Taxis are worth their weight in gold for short hops in the cities. Dragging luggage thru the street while you try to find the hotel aint no fun at all!

When you say "Yokohama Port", do you mean you will be arriving on a cruise ship? If so, I guess you might be arriving at Osanbashi Pier, so the nearest station is Nihon Odori on the Minatomirai Line. This will take you directly to Shibuya in central Tokyo, but I'm not sure wher you mean by "Tokyo Intercontinental Hotel", as there appear to be several in Tokyo (ANA in Akasaka and Tokyo Bay in Hamamatsucho), as well as the one in Yokohama in the Minato Mirai area. So you will need to be more specific if you want more precise directions.

If you're headed to the ANA Intercontinental in Akasaka, take the JR Tokaido Line or JR Yokosuka Line from JR Yokohama Station to Shinbashi (450 yen) Station (no transfers) then take a taxi to the hotel. Otherwise, you will have to transfer to a Metro subway line and lug your baggage up the stairs out of the stations.

Once again thanks for the valuable info.

In that case, you should get a taxi to Yokohama station, catch a JR Tokaido Line train bound for Tokyo station as far as Shimbashi station, and get a taxi to the hotel from there. The JR Keihin-Tohoku Line suggested by the posters above can also be used, but stops at every station along the way, and takes a good 10 minutes longer.