A cruise is not the best way to try to see the Northern Lights, as Southeast Alaska and the Inside Passage are too far south for reliable aurora displays. You need to be farther north and in area that is as cloud-free as possible. Fairbanks is the best place for most people for aurora hunting. I lived there for seven years ( six winters) and I can tell you that seeing a good aurora is never guaranteed, whether you stay for a weekend, a week, or maybe even a lifetime. I was fortunate to see some of the best, full-color displays, but you have to be determined and willing to stay up til 2 or 3 am sometimes. Or request a wake-up call from your hotel.
According to the University of Alaska Geophysical Institute, whose job in part is to study of the aurora, the best time and place to hunt for the aurora is Fairbanks during dark if the moon in March.
http://auroraforecast.gi.alaska.edu/travelers-guide.php
That is due to a combination of factors, including moderating temperatures ( less likely to be forty below zero), adequate length of darkness, and others.
They also publish a forecast, and if you follow it regularly, you will see that most of the time the forecast is for low or moderate activity. This means you may see a glow in the sky or maybe some dancing lights with faint reddish or green color, but nothing spectacular.
http://auroraforecast.gi.alaska.edu
The best place to stay is north of town in a lodge or cabin that is well away from city lights and has a clear view of the sky ( away from trees that obstruct the view). There are lodges dedicated to the aurora experience, including one with glass roof, and tours that focus on seeing the Lights. Just remember that they are not guaranteed at any time. All you can do is make choices that maximize your chance of seeing a good aurora, and hope for the best. And find something fun to do during the daytime, like snowshoeing, Nordic skiing, dog sledding, etc. and study up on how to stay warm when it is really cold outside.