If you were traveling from the Panama canal to Long Beach would you rather your balcony cabin be on the port/left side or starboard/right side? The hot afternoon sun makes me think I'd rather be on the starboard side facing land. This will be in March.

I have never based my cabin choice on the side. That said, I generally prefer the side that doesn't get the morning sun, but that can change from day to day depending on the route. For scenic cruising, you probably won't be in your cabin anyway.

We and our binoculars spend a lot of time on our balcony, so I prefer mostly land side, though it can change over the course of a cruise.

My thoughts too.

In my experience, ships seem to sail pretty far away from land so it's barely visible if visible at all, unless the ship is starting or heading for a port. I'd choose based on desire for or lack of solar exposure.

Depends on the cruise itinerary. Through the Panama Canal, on Alaska cruises, in Asia when we sailed up rivers to Bangkok and Ho Chi Minh City - the kinds of cruises we prefer - yes, we are quite close to shore and again, do spend a LOT of time on our balcony with our binoculars. So for us, it makes a difference. Oh, also, we're typically on small(er) ships.

We acknowledge we spend much more time on the balcony than most people on a cruise, and that's ok - I don't really care what other people are doing ;-) We might be the only people who plan like this ;-) But OP did ask, and this is my experience.

Our thinking (Canucks who like oceans but not heat and humidity)
For southern itineraries, we generally look for sun in the AM vs PM- we find the balcony becomes unbearable otherwise.
The only time this backfired on us was a Jan cruise up the Pacific coast from Mexico- shady starboard side was cold in the pm! like wear a hoodie and blanket cold...
In port, it is difficult to know which side is the 'warm' side. This is important as when there is no breeze, the sun plus humidity are deal breakers for sitting outside.

For our Panama Canal full transit, a balcony cabin was a must- it's been a few years, but in one of the locks close to Panama City, we could have 'reached out and touched' the wall... I believe different routes (partial/full transit) would use the old vs new canal so your experience may differ.