2011 Macbook Air connects to WiFi but can't get Internet
As you say this only happens with Hotel Networks.

Usually the process with Hotel networks is 2 steps.

1- First you log in to they WiFi

2- Once logged in, the Hotel Server will send you a "Captive Portal" web site, on which you must continue to get Internet access. I assume you do not get t this step (no portal showing)

Your Mac (for your protection) before that popup shows, will check the certificate revocations to verify the popup being shown isn't a fake one.

Fixing it:

Usually there is simple fix to show the Captive Portal by just entering cnn.com in your browser and it will redirect you to the Captive Portal, but not always.

Try with different browser open.

Alternative solution is to create a "new location" in the network system preferences window, name it Hotels if you whish, and remove all DNS servers.

Similar problem and solution described here https://apple.stackexchange.com/a/37851/46541