I'm not too sure how to go about getting the external IP address of the machine as a computer outside of a network would see it.
My following IPAddress class only gets the local IP address of the machine.
public class IPAddress {
    private InetAddress thisIp;
    private String thisIpAddress;
    private void setIpAdd() {
        try {
            InetAddress thisIp = InetAddress.getLocalHost();
            thisIpAddress = thisIp.getHostAddress().toString();
        } catch (Exception e) {
        }
    }
    protected String getIpAddress() {
        setIpAdd();
        return thisIpAddress;
    }
}