A few weeks ago, my wife and I released A Short History of Virginia City, which addresses this very question. But the question - as you suggest - is greater than one that might fit only Nevada; it is a matter for all of humanity to consider regardless of the location.

As the debate - to which you refer - has raged and infuriated residents of the disputing communities, the question of the definition and "settlement" and "town" has lurked as the linguistic underpinning of the dispute. If we can agree on the following, it seems to me the answers are quit simple:

A "settlement" is a place where people live, and if we want to talk about a permanent settlement, it is a place that is/was inhabited all year round.

A "town" is a settlement that includes some of the clear markers of organized community. In the American West, that was often first defined by a post office, but other things includes schools, churches, or structures for local government and/or courts fit the bill as well.

With that, this is what my wife and I concluded:

"To this day, there is a dispute with Genoa, to the southwest [of Dayton] at the foot of the Sierra, as to which place deserves the title of Nevada's oldest community. Genoa had a post office and other hallmarks of a town before Dayton, but the latter was apparently the first to have year-round inhabitants. Consequently, it is possible to assert that while Genoa is Nevada's first town, Dayton is the region's oldest European American settlement."

I have heard Genoans assert that Dayton may have been settled year-round, but that doesn't count because they were just a bunch of dirty, smelly miners. Fortunately, we don't normally judge the definition of a thing associated with the settlement and organization of humanity by its cleanliness or smell.

I hope this helps you, but I anticipate the dispute to rage for another few centuries, regardless of anything I assert in print.