Welcome to the Japan Forum.
Your question on the "fastest way" is relative to many factors.
But first and foremost
DO NOT TAKE A TAXI.
Your options to/from NRT can be found here:
http://www.flyertalk.com/forum/showthread.php?t=530019
I recommend taking the Airport Limobus direct to the Westin, If you go by train you have to make at least 1 connection, and walk about 10-15 minutes from Ebisu Station (the closest station to the hotel) to the Hotel.
As I mentioned before the "fastest way" is relative. On paper the train appears to be fast, and yes the Narita Express is the fastest way into Tokyo Station from NRT. However, factor in the connection time, at Tokyo Station to the Yamanote Line, or the connection time at Shinagawa Station, then the time it takes to walk from Ebisu Station to the hotel (again its about a 10-15 minute walk), time wise, taking a limobus from the Airport is just as fast, plus you don't have to bother with any connections.
You can ride to Tokyo Station or Shinagawa Station, then connect to a Taxi, but why do that when you can take a direct bus and pay alittle less? Plus the time difference in any option will be very great.
I need to get to the Westin which I think is by the water.
The Westin is in the middle of a Urban area, I think the only water its close by is its swimming pool.