How to get the IP address of the server on which my C# application is running on?

Nope, that is pretty much the best way to do it. As a machine could have several IP addresses you need to iterate the collection of them to find the proper one.

Edit: The only thing I would change would be to change this:

if (ip.AddressFamily.ToString() == "InterNetwork")

to this:

if (ip.AddressFamily == AddressFamily.InterNetwork)

There is no need to ToString an enumeration for comparison.

The only way to know your public IP is to ask someone else to tell you; this code may help you:

public string GetPublicIP()
{
    String direction = "";
    WebRequest request = WebRequest.Create("http://checkip.dyndns.org/");
    using (WebResponse response = request.GetResponse())
    using (StreamReader stream = new StreamReader(response.GetResponseStream()))
    {
        direction = stream.ReadToEnd();
    }

    //Search for the ip in the html
    int first = direction.IndexOf("Address: ") + 9;
    int last = direction.LastIndexOf("</body>");
    direction = direction.Substring(first, last - first);

    return direction;
}

WebClient webClient = new WebClient();
string IP = webClient.DownloadString("http://myip.ozymo.com/");

using System.Net;

string host = Dns.GetHostName();
IPHostEntry ip = Dns.GetHostEntry(host);
Console.WriteLine(ip.AddressList[0].ToString());

Just tested this on my machine and it works.

namespace NKUtilities 
{
    using System;
    using System.Net;
    using System.Net.Sockets;

    public class DNSUtility
    {
        public static int Main(string [] args)
        {
            string strHostName = "";
            try {

                if(args.Length == 0)
                {
                    // Getting Ip address of local machine...
                    // First get the host name of local machine.
                    strHostName = Dns.GetHostName();
                    Console.WriteLine ("Local Machine's Host Name: " +  strHostName);
                }
                else
                {
                    // Otherwise, get the IP address of the host provided on the command line.
                    strHostName = args[0];
                }

                // Then using host name, get the IP address list..
                IPHostEntry ipEntry = Dns.GetHostEntry (strHostName);
                IPAddress [] addr = ipEntry.AddressList;

                for(int i = 0; i < addr.Length; i++)
                {
                    Console.WriteLine("IP Address {0}: {1} ", i, addr[i].ToString());
                }
                return 0;

            } 
            catch(SocketException se) 
            {
                Console.WriteLine("{0} ({1})", se.Message, strHostName);
                return -1;
            } 
            catch(Exception ex) 
            {
                Console.WriteLine("Error: {0}.", ex.Message);
                return -1;
            }
        }
    }
}

Look here for details.

You have to remember your computer can have more than one IP (actually it always does) - so which one are you after.

Yet another way to get your public IP address is to use OpenDNS's resolve1.opendns.com server with myip.opendns.com as the request.

On the command line this is:

  nslookup myip.opendns.com resolver1.opendns.com

Or in C# using the DNSClient nuget:

  var lookup = new LookupClient(new IPAddress(new byte[] { 208, 67, 222, 222 }));
  var result = lookup.Query("myip.opendns.com", QueryType.ANY);

This is a bit cleaner than hitting http endpoints and parsing responses.

private static string GetLocalIpAdresse()
    {
        var host = Dns.GetHostEntry(Dns.GetHostName());
        foreach(var ip in host.AddressList)
        {
            if (ip.AddressFamily == System.Net.Sockets.AddressFamily.InterNetwork)
            {
                return ip.ToString();
            }
        }
        throw new Exception  ("No network adapters with an IPv4 address in the system");
    }