Often I find that when I’m trying to access hotel WiFi, I get assigned a TCP/IP address that starts with 169. The Apple network setup complains that this is a “self-assigned” address, and it don’t get any Internet access in any case.
The universal solution to this problem appears to be simply to power the WiFi access point off and on. Sometimes this is easy to do yourself (hint: often the access point is hidden under the desk in the hotel room); other times you have to ask the hotel staff.
I just had to do this at Club Quarters in New York: there’s a little SMC access point on the desk in the lounge; I unplugged the power, plugged it back in and, presto, working WiFi.