I don't know how accurate this is for Japan but I've used the website for other countries:

http://www.taxifarefinder.com/main.php?city=Tokyo-Japan

It will be well over $200 dollars. Take the Airport limo bus for about $30

...and take a taxi from there. email your hotel and they should be able to tell you which limo bus.

The Narita Express train goes to Shinagawa Station which is a block from your hotel - couldn't be much easier....enjoy!

Airport limo bus goes to the hotel. Here is the schedule:
http://www.limousinebus.co.jp/en/platform_searches/index/2/41

I think this hotel is across the street from Shinagawa station.

Or maybe a block as Mara wrote.

I was thinking of the Shinagawa Prince Hotel. The Grand Prince Takanawa is farther from the station. I think it is up a hill.

Here is a map of the area:
http://www.booking.com/landmark/jp/shinkansen-shinagawa-station.en.html

Mouse over the hotel icons and it shows the names.

The hotel's website says:
"A 5-minute walk from the Takanawa exit of Shinagawa Station..."

Is that the Japanese local five minute walk or the gaigin lost looking in every direction for five minutes walk?

Aloha!

lol, ht, that is from the hotel's English language website so I assume it's for the lost 外人 (gaijin)

A 5-minute uphill walk, hauling luggage, maybe in the dark, maybe raining or cold or both, after a long flight and ride on the N'Ex would not be my plan given that the bus goes door to door. Maybe if I wanted to use a JR Pass to save the yen, but even then maybe not.

First I would say DO NOT TAKE A TAXI!!!! It will set you back over $200 and I don’t know about you but upon arrival I think you want to hold on to your yen.
Using Hypwerdia.com to check train schedules, routes and fares I came up with the following suggestion for you.
Fare ranging from ¥1,390;92 Minutes;Transfer: 1 Time to ¥3,110;77 Minutes, Transfer: 0 Times
http://www.hyperdia.com/en/
Hyperdia is very user friendly and you can input the information you have such as date and time you want to use the train and you will get several route suggestions. I would recommend using the route that doesn’t require you to transfer but even if you do, the Japanese people are wonderful at helping the lost gaijin. Get some more specifics from your hotel if you can and just remember to triple whatever walking time they give you.
I’m with ht about the walking. Japanese walking time is in my estimation 1/3 of American time. I even joke about it with my Japanese friends when they give me directions. I always ask them to translate it to “American walking time”. They laugh and reluctantly triple it .