You want to know the city, given a set of latitude/longitude coordinates.
This is called reverse geocoding.
This is usually accomplished by using a web service. Many providers offer this for free, although usually with some limitations.
The Google Geocoding API[
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MapQuest Geocoding API[
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MapQuest Open Geocoding API[
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Yahoo BOSS Geoservices[
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Bing Maps REST Services[
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7 free Geocoding APIs[
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Many of these offer .NET APIs, and if they don't there are usually 3rd-party APIs, including some on this website.
Performing this task offline is generally not done, however you can purchase databases that will facilitate doing so.