After beating the Koopa Brothers, there wasn’t an immediate clue where I should be going next. And so I didn’t really go anywhere. I spent half an hour retracing my steps to see what I was missing.
What I was missing, apparently, was that there was a new area opened up to the south of Toad Town. It wasn’t immediately obvious to me since I had been told about the port many days beforehand and I just forgot. I don’t like having to resort to a walkthrough, but unfortunately real life just means I can’t remember offhanded comments from random characters between play sessions.
So, off to the desert now.