You’re probably familiar with whatismyip services. One problem with these is that they wrap the IP data in a visually-pleasing but impossible to parse smorgasboard of HTML.
I needed to determine external IP for a text-only host with somewhat limited tools, and I came across the wonderful ifconfig.me page. This basically does the same as whatismyip but with lightweight and easily parsable output. This, for instance, returns *only* the system’s external or public IP address:
Several endpoints are provided for you to poke at your connection’s externally-visible information. For the ultimate in parsability and machine-readability, a complete json dump is provided here: http://ifconfig.me/all.json.
Recently I’ve had better success with http://ifconfig.co which works mostly similarly to ifconfig.me but is a bit faster.