In order to convert a point into a city name, you'll have to reverse
geocode the point. Usually this takes a database of the cities of
interest in the form of a polygon of the city boundaries and using
some sort of software (like Postgresql) to discover what polygon
(city) the point is contained within. The geonames.org site has some
excellent data and the price is right (free) but using it may be a
problem if you are unable to implement the programming required to
make it work.

There is no issue with the "perfect match" of coordinates that you're
talking about. What you need is for your database of polygons to be in
the WGS84 coordinate system and if you use points generated from a
Google API based map, you should have that "perfect match" you seek
without doing anything.

I believe geonames.org has data for your country, but if not, you can
develop it yourself by using one of the polygon tracing programs
available free, manually tracing boundaries around each city of
interest and saving those to a database. While this might seem like a
lot of work, it probably is the best solution if you want to have
accurate and maintainable data. There also might be this data
available from a government body somewhere. You'll have to do the
research on that yourself. The US has great stores of this type of
data for free, so Ecuador may also, only way to find out is to start
searching (Google is your friend).

-John Coryat

http://maps.huge.info

http://www.usnaviguide.com
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