Face forward (that would be the pointy end of the ship) and to your right is starboard, to your left is port. Now that we've established that, which side of the ship is "best" for your itinerary? Over the years that question has come up frequently. My answer generally isn't very useful in terms of cabin selection. You see, it's impossible to say which side of the ship is "better" in terms of cabin selection.
Ships don't always receive the same berthing assignment in ports of call and the side of the ship that faces land and/or the dock isn't always the port side of the ship. Even when a ship calls at the same port every week and there's only one berth, like Disney's private island Castaway Cay, even wind and wave conditions can change the berthing arrangement. I know of one cruiser who selected cabin locations on Disney Wonder based on past experience and then during the docking procedure at Castaway Cay was dismayed that the ship backed into its berth instead of nosing in as it had done on previous cruises.
In the case of Castaway Cay, cabins on both sides of the Disney ships have a decent enough view because of the scenery. That isn't always the case, though. Some ports of call, particularly those in Europe, are fairly industrial and there isn't much to see. If your cabin has a balcony, being on the side of the ship facing the dock is fun when sailaway time draws near and fellow passengers are scurrying back to the ship—such as late afternoon in Cozumel. As amusing as your fellow passengers can be, if your ship overnights at the downtown Cozumel pier your balcony facing town has a view, but it can be a noisy one when the music cranks to high volume at the clubs near the end of the pier.
While it's difficult, if not impossible, for me to say that port or starboard is "best" for any particular itinerary, I can happily share my Tips for Selecting a Cruise Ship Cabin.