Well, we completely changed our plans for Japan. Now, we are booked on a cruise at the beginning
and we have a very specific question.
We arrive at Narita Airport on April 19th. And our cruise leaves from Yokohama on the 20th. It looks like the best way to get there would be by train? However, we will have a fairly large suitcase each. I don't want to
be hauling them up stairs. So, first do the stations have elevators? and secondly, is there a better alternative without costing $ 300.00 for a private van, which is what I got from Viators?? We do not want to rent a car because of the stress of driving on the left.
Any help is appreciated!!

http://www.yokohamajapan.com/transpo...g-to-yokohama/

See above for possibilities...don't know where you are staying or where your port is....

All stations have elevators and/or escalators. They can be a bit tricky but they all have them. It's very easy to travel by train and so I wouldn't even consider a van or rental car. The bigger concern would be transit in Yokohama- the easiest way to do it would probably be stay at a hotel very close to Yokohama station and then take a taxi from your hotel to the port.

Depending on your arrival and departure times, you might be able to take advantage to Japan's excellent and reliable luggage-forwarding option. It's called takuhaibin; here's the info:
http://www.japan-guide.com/e/e2278.html

The cruise ship pier is called Osanbashi; it's in the red warehouse district. It's a $15 taxi ride from Yokohama station or YCAT and the same or less from the main hotels in Yokohama. The Narita Express goes direct to Yokohama from Narita and the Keikyu trains do the same from Haneda.

However, your best bet is to take the limmo bus from the airport to a hotel in Yokohama (e.g., the Intercontinental is close to the pier), overnight there, and then a taxi to the pier in the morning.

Do not try to walk to the pier from the Osanbashi bus stop or the Nihon Odori subway: it's further than it looks, and uphill.

With luggage as you described, I would take the limo bus to hotel and then taxi to port, as someotherguy suggested.

You can get timetables here:
https://www.narita-airport.jp/en/access/bus/

Under "Area", choose Yokohama and then it doesn't matter what terminal you choose. Click under Arrival and you will see which hotels are served directly.

They are:
Yokohama Bay Hotel Tokyo
Intercontinental Yokohama Grand
Yokohama Royal Park
Hotel New Grand

The first three hotels are in the same area. Am pretty sure they are in the area with the building that looks like a watermelon slice - that building, I think is the Intercontinental Grand.

The Hotel New Grand is closer to the cruise terminal, but I definitely like where the other three are.

The watermelon slice is the IC Grand. It is on the left in this photo: http://www.interconti.co.jp/yokohama...ndex_ph001.jpg

If the limo bus to hotel timetable didn't work for me then I would take one to the YCAT and taxi from there to one of the hotels above. It should be easy enough to navigate to a taxi stand by following signs.

Actually finding your way to a station hotel can be tricky. It is a big confusing station. There is a Sheraton nearby but it takes a bit of effort to find and get to. I also stayed at a hotel that was down the sidewalk (IIRC) from the west side of the station, in the same block more/less, but I would not recommend it for you.

The limo bus to hotel plan is a no-brainer.