I almost always clear south of the market, but I usually kill one or two monters north of the port square as well as one or two more on the square to the east of the port square before I reach the market square. There is a perfectly logical reason for this.
I carry a miracle satchel. When I arrive at the port, I'm always full health. If I immediately move east, my miracle satchel won't be able to take effect since I'm at full health. Therefore, I fight monsters north of the port until I am at least two miracle satchel doses down from my max. I then move once to the east (miracle satchel takes effect), then attack to the south (miracle satchel takes effect again, meaning I'm almost at full health before the fight begins).
Similarly, I fight monsters on this middle square until I'm at least two miracle satchel doses down from my max again, then move to the market square to continue my relentless assult to the south.
This saves a maximum of two clicks per trip to the island. This isn't much in the big picture, but once the strategy is known and understood, it's silly not to use it.
Sandy