This question was marked as off-topic at SuperUser and StackOverflow, if this is the right place, please let me know so I can edit the post and place the question here. https://superuser.com/questions/809489/website-with-memorable-static-ips-to-test-connectivity
No, it's not on topic on the network engineering stackexchange. If it's not on topic on superuser I can't think of an appropriate stackexchange.
It's quite on topic, the ability to test general internet connectivity is relevant to network engineering.
220.127.116.11 is Google Public DNS. Pings and DNS requests to this should succeed. This is meant to be public and used.
18.104.22.168 and 22.214.171.124 are Level 3 Communications DNS servers. Pings to these should succeed in general; DNS requests may. These are not necessarily intended to be public, but Level 3 has not locked them down and these are generally used in troubleshooting by techs and network admins worldwide.
With these you should be able to prove Layers 1-4 (DNS being UDP on port 53, that covers you to Layer 4). This should prove your config, and effectively prove surf. You may even set up track/IP SLA statements to 126.96.36.199 to track WAN availability (and kick off backup circuits etc), though there could be ethical problems with that since it's meant to be public DNS, not a general public ICMP responder.