- I opened System Preferences » Network » Airport » TCP/IP tab and set the configuration to manual. Then I set the IP address to 192.168.1.10 and the router to 192.168.1.1.
- I set the DNS servers to 4.2.2.1 and 4.2.2.2, separated by a return (this is a key step!)
- I then opened Terminal and ran ping 192.168.1.1 to see if I magically guessed the correct router. I didn't (no return ping). So, I changed my IP address to 192.168.2.10 and the router to 192.168.2.1. I tried ping again, and I got a ping back.
- Now, I realize that I'm messing with DHCP settings, so to be fair, I pinged 192.168.2.11, and when I didn't receive a return ping, I then changed my IP address to 192.168.2.11 in case 192.168.2.10 had already been given to another computer on the network. (I suggest continuing to ping 192.168.2.x up the line until you don't get a return ping).
Side note: I actually figured out that the router the hotel was using was a Linksys WRT54g. I typed 192.168.2.1 into my browser window, and the login for that router popped up. An internet search yielded many WEP issues for Macs, and the suggestion was to use a WPA key instead of a WEP key, which isn't feasible if you're on a hotel network.

