I have a few interesting domain names I picked up when I owned a cloud hosting business. Those days are long gone, but you never dump your domains. For cheap at least.
So there are apparently plenty of sites that will show your public IP address. I learned as much posting to /r/devops on Reddit the other day. However, if you want a easy to remember domain name that will return your public IP with no ad’s and crap just type https://damninter.net into your browser or favorite CLI utility to get your IP address.
To ensure uptime I have placed it behind a load balancer and since it’s on AWS, you can get some AWS specific results. Some have found some interesting paths out of their VPC’s being different than what they expected.