After only three hours of struggling, I managed to get my xbox connected to the internet! Really, it wasn't meant to connect to hotel-style wifi where you need to log into a browser and accept the terms/conditions before being granted access.
The basic instructions are here:
http://sacramentocomputerhelp.com/xbox360answers.html#troubleshooting. At first, I seemed to have to reshare my wifi connection every time I turned on my xbox, but that seemed to disappear later on. I'll have to see if that's really the case. I was able to get general connectivity fairly easily, but it only gave me three tabs, and didn't give me any of the cool stuff like marketplace or netflix. This was due to error 80072ee2, which basically indicates that it doesn't have access to all the ports it requires. A handy post from Microsofot told me what ports Xbox required.
http://support.microsoft.com/kb/908874/ I tried opening the ports through internet connection sharing, but that didn't seem to be the problem. I then tried a port scanner and found that several of the ports were blocked by what I thought was Wayport (the wifi internet provider at the apartments I'm staying at). I looked around a bit and found a list of ports that they claimed to be blocking and I should have been fine. I then remembered that (duh!) my computer has a firewall. So I opened the ports in the firewall, but no luck there either.
Finally I did the unthinkable and just turned off the firewall. Yep, that worked. So I sat down and watched an hour of netflix while (theoretically) zillions of hackers compromised my system.
I'll have to play with it a bit more tonight to see if I can put the firewall back up and still have everything working.