Hope this reply finds you doing well. In regard: "I would like to set static IP addresses on both linux boxes so that I do not have to change /etc/hosts when DHCP changes their IP" which flavor of Linux do you have? If you have red hat like flavors (Fedora, CentOS) you need to use directory (CentOS) /etc/sysconfig/network-scripts/ifcfg-eth?(?=number of ethernet adapter). Also you can use the network connections tools.
Now, if you want to set a static public IP, then that's another story. You can use tools such as: http://www.whatismyip.com/ to find your public IP, but they change. If you are a business and want to get a static IP for web hosting, then you need to go to an ISP.
I hope this is some help. Take care.