Public IP Capture Program

The most direct way to get your public IP is - as you suggested - access a website that will return this information to you. If there are no drawbacks, why not your own website / application?

But if you need an external service, there are several that you choose - not all so simple to use and / or free (whatismyip.com for example has an API, but only for a paid plan, and with requests limit daily). Here are some options , the simplest and "no frills" being the icanhazip.com (or canihazip.com/s ) - it returns you IP and ready, without html , body , or anything! So to access it just do:

URL url = new URL("http://icanhazip.com/");
BufferedReader in = new BufferedReader(new InputStreamReader(url.openStream()));
String ip = in.readLine();
in.close();

Maybe it's interesting - if your primary source is offline - try some alternative sources. Others that return the raw IP are ifconfig.me/ip and the ipinfo.io/ip (same procedure above).

Source: this question in SOen

If it is HTTP, just do the following servlet

package servlet;  

import java.io.IOException;  
import java.io.PrintWriter;  
import javax.servlet.*;  
import javax.servlet.http.*;  

public class ServletIP extends HttpServlet   
{  
   private static final String CONTENT_TYPE = "text/html; charset=ISO-8859-1";  

   public void init(ServletConfig config) throws ServletException  
   {  
      super.init(config);  
   }  

   public void service(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException  
   {  
      response.setContentType(CONTENT_TYPE);  
      PrintWriter out = response.getWriter();  
      out.println(request.getRemoteAddr());  
      out.close();  
   }  
}  

And then the mapping:

<servlet>  
  <servlet-name>ServletIP</servlet-name>  
  <servlet-class>servlet.ServletIP</servlet-class>  
</servlet>  
<servlet-mapping>  
  <servlet-name>ServletIp</servlet-name>  
  <url-pattern>/ip</url-pattern>  
</servlet-mapping>

Loading this on a Java EE server, sending any request to www.ENDERECOWEB / context_con_container / ip, it returns the person's IP address.