Most cities seem to follow the Cartesian coordinate plane you mentioned in your question. Something Wikipedia agrees with, in its section on Street or road name Grid-Based Naming Systems section.
In many cities laid out on a grid plan, the streets are named to indicate their location > on a Cartesian coordinate plane. For example,
the Commissioners' Plan of 1811 for Manhattan provided for numbered
streets running parallel to the minor axis of the island and numbered
and lettered avenues running parallel to the long axis of the island,
although many of the avenues have since been assigned names for at
least part of their courses. In the city plan for Washington, D.C.,
north-south streets were numbered away from the United States Capitol
in both directions, while east-west streets were lettered away from
the Capitol in both directions and diagonal streets were named after
various States of the Union. As the city grew, east-west streets past
W Street were given two-syllable names in alphabetical order, then
three-syllable names in alphabetical order, and finally names relating
to flowers and shrubs in alphabetical order. Even in communities not
laid out on a grid, such as Arlington County, Virginia, a grid-based
naming system is still sometimes used to give a semblance of order.
Often, the numbered streets run east-west and the numbered avenues
north-south, following the style adopted in Manhattan, although this
is not always observed. In some cases, streets in "half-blocks" in
between two consecutive numbered streets have a different designator,
such as Court or Terrace, often in an organized system where courts
are always between streets and terraces between avenues. Sometimes yet
another designator (such as "Way", "Place", or "Circle") is used for
streets which go at a diagonal or curve around, and hence do not fit
easily in the grid.
In many cases, the block numbers correspond to the numbered cross
streets; for instance, an address of 1600 may be near 16th Street or
16th Avenue. In a city with both lettered and numbered streets, such
as Washington, D.C., the 400 block may be between 4th and 5th streets
or between D and E streets, depending on the direction in which the
street in question runs. However, addresses in Manhattan have no
obvious relationship to cross streets or avenues, although various
tables and formulas are often found on maps and travel guides to
assist in finding addresses.
However, like any naming convention, it is simply a convention, and is not necessarily applied everywhere. There is a long discussion here on MetaFilter on this topic that contains many examples where the opposite is the case e.g. Large Road and Small Road or East-West and North-South like in Chicago.
Numbered streets then named streets seems to be the most common. If your town has those, then that should be your answer. If not, then it's a matter of stylistic preference.
Best Answer
The label placement is often designed to improving map readability rather than being driven by the data directly: often cartographic displacement is performed on the original geometries to improve the legibility of the map. 41Latitude had a great article on city label placement you might be interested in.
The USGS GeoNames aka GNIS (a commonly used public domain gazetteer used by e.g. Geonames.org, Wikipedia, OpenStreetMap) provides this note:
If you were looking to algorithmically choose the center of a city you might use the centroid of a polygon delineating the city limits, or perhaps something more sophisticated like using the center of the alpha shape.