The problem is that you are mixing up options of the library with HTTP headers. Try with this instead:
public static void Main (string[] args)
{
string url = "https://dashboard.reviewpush.com/api/company/locations";
using (var client = new WebClient())
{
client.Headers[HttpRequestHeader.ContentType] = "application/json";
client.Headers["X-Api-Key"] = "key";
client.Headers["X-Api-Secret"] = "secret";
string s = client.DownloadString(url);
Console.WriteLine(s);
}
}
You might want to look into the recommended HttpClient
if you can use .NET 4.5 or newer.
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solved How to call third party Restful API [closed]