A ship can tie up on either side and could face either into or out of the port - so one side does not consistently have better views in port. Once you're in the open ocean, the view will be pretty much the same on either side - ships really don’t often sail that close to shore. If you’re arriving into port or cruising near somewhere amazing - past Stromboli volcano for example - then you want to be up on deck, looking forward to see the all ocean around you, to make sure you get the full experience! For this you can either go high to the top decks or search out a lower viewing deck that’s open to passengers - the helipad at the bow is very popular but you may need an invitation or a pass. When Cruising in an inlet - say into the Fjords, Kotor or parts of Alaska - the ship will go in facing one way and come out facing the other, so both sides will get the best view at some point! And for some ‘scenic cruising’ such as in Hubbard Glacier the ship actually turns gently in a full 360* circle so everyone will get the same view from their balcony.

I love sunsets and am fairly unlikely to even see the dawn so on a passage - a cruise that start in one place and ends in another - there will generally be a side that will get better sunsets. On these itineraries, choose a port side cabin for sunsets if you're sailing north or west, or to see sunrise if you're sailing south or east (or choose starboard for the opposite). But most cruises go out and round and back to where they started so then it really won’t matter at all
There are a couple of specific places it could make a difference …