(Its from my experience people use the term "subway" for everything mass-transit, normally its fine for cities that have one primary rail operator, but when it comes to Japan, and Tokyo especially, a distinction needs to be made in order to avoid confusion with subways, and regional rail operators, for example if someone asked directions by "Subway" to Shinjuku from Tokyo, you can take Tokyo Metro "subway" from Tokyo to Shinjuku, alternately, you have a non subway route, take the JR Chuo line. Depending on how or where you ask, someone might give you one option or both options. The JR Pass is not valid on subways, monorails, etc in Japan, but rather only on trains operated by JR, Japan Railways, with some exceptions)
An alternative you have is when you reach Tokyo by Narita Express, either at Tokyo, Shinagawa, or even Shinjuku Station, you can switch to the JR Yamanote line (local train) to Ebisu Station and walk to the Westin (about 10 or so minutes walk).
I understand what you mean with luggage, the same principle is the same, from subway, or local JR/private rail trains, if you have a lot of luggage you do not wish to mess with the crowds, stairs, escaltors etc and lugging things around on a local train, then you might want to consider a taxi from the station to complete your trip.
I would say taking a taxi from Shinagawa Station to Ebisu, where the Westin is, would be a little cheaper than a taxi from Tokyo Station. But I'm not too sure on this matter.
I agree with abmj-jr:
The limobus is a good option for those who just want to let someone else worry about the navigation and who have lots of bags. My option is always the train+cab (or subway), but I never have much luggage and love to watch the scenery go by on the train. If your hotel is the last stop, the bus will take longer, but deliver you right to the hotel. On the train, you will need to transfer selves and bags to a cab. Each has advantages and you know how you travel best.