That will only keep your DNS servers from going down.
What you're looking for can't really be done with the level of control you have over the network. You can do round robin requests, as in
www.site.com has two IP addresses, but when one goes down, roughly half of the requests will fail. You need to use some fancy routing/dns tricks to get geographically distributed high availability. What most sites do is put 2 servers in a good data center, stick an http load balancer in front of those, and call it good.
etc, etc, etc.
This is a pretty big topic though, I'd suggest doing some reading on how to run a highly available web site.