if your getting an ip then you may have DNS issues. Firstly: are you sure its an open AP at a hotel? maybe they have not opened your account to use it. just because the AP does not ask for a passphrase does not mean its open.
anyways, try pinging your gate way to see if you are actually on the intranet first
@monk ~]$ route
Kernel IP routing table
Destination Gateway Genmask Flags Metric Ref Use Iface
192.168.1.0 * 255.255.255.0 U 2 0 0 wlan0
default 192.168.1.254 0.0.0.0 UG 0 0 0 wlan0
the gateway address in my case is highlighted in yellow. So, now just type ping at the prompt followed by the gateway ip address and see what happens. if that DOES work then try
@monk ~]$ ping www.yahoo.com
if you dont get a response to the web site then it is a DNS issue. However, if you dont get a response to the gateway ping attempt then you got something else going on and adding public DNS servers will be a wast of your time.
you could try some open DNS servers and place then in your network config ( you didnt state the os your running). you can get some at this link @ http://www.dnsserverlist.org/
thats if your actually gettitng an ip .