This is probably what you are looking for (one of the code snippets does exactly what you want).

As for services/websites you can query to get the public ip address, here's a short list (you'll have to modify the example above to parse the response correctly):

http://checkip.dyndns.com
https://www.whatismypublicip.com/
http://freegeoip.net
https://who.is/
http://www.ipchicken.com/
http://www.whatsmyip.org/
https://api.ipify.org/
https://whatismyipaddress.com/

IMHO, the simplest is api.ipify.org.  However, note that some of those service also answer geolocation info!