Javascript Deserializer not working on my json object - ASP.Net API Application

What am I doing wrong?

A lot, actually. Starting with: your WeatherInfo. It's all wrong - the JSON serializer needs an object that matches the JSON, or has attributes indicating why it doesn't match the JSON. Your object does neither.

In order to work it, we need the objects to match up, the following POCO's should work:

public class WeatherInfo
{
    public Coordinate coord { get; set; }
    public Weather[] weather { get; set; }
    public string base { get; set; }
    public MainInfo main { get; set; }
    public float visibility { get; set; }
    public WindInfo wind { get; set; }
    public CloudInfo clouds { get; set; }
    public long dt { get; set; }
    public SysInfo sys { get; set; }
    public int id { get; set; }
    public string name { get; set; }
    public int cod { get; set; }
}
public class SysInfo
{
    public int type { get; set; }
    public int id { get; set; }
    public float message { get; set; }
    public string country { get; set; }
    public long sunrise { get; set; }
    public long sunset { get; set; }
}
public class CloudInfo
{
    public float all { get; set; }
}
public class WindInfo
{
    public float speed { get; set; }
    public float deg { get; set; }
}
public class MainInfo
{
    public float temp { get; set; }
    public float pressure { get; set; }
    public float humidity { get; set; }
    public float temp_min { get; set; }
    public float temp_max { get; set; }
}
public class Weather
{
    public int id { get; set; }
    public string main { get; set; }
    public string description { get; set; }
    public string icon { get; set; }
}
public struct Coordinate
{
    public float lat { get; set; }
    public float lon { get; set; }
}

Once you've done that, it should be trivial to navigate the information to collect what you want. You should also consider looking up what attributes your serializer may use so that you can name these properties in accordance with .NET naming conventions, and use the attribute to specify what JSON name they have. The JSON.NET and JavaScriptSerializer items both support various attribute types to do this, if you're using a home-brew serializer you may or may not have one, but it looks like you're using the built-in JavaScriptSerializer, so I recommend you look up the attributes it uses and update these models in your work accordingly.