On a recent business trip, I left town with my iPhone 5, Nexus 7, laptop, and Chromecast (I only take the Roku on longer trips.). This trip though was my first with the TP-Link WR-710N travel router. I bought this on a whim when it came up for cheap on Lifehacker's daily deals. My initial thought was that I could set it up identically to my home SSID and plug in the hotel's wired port.
At this particular hotel though, there were no wired ports so I had to use another feature of this router. It has a WiSP (Wireless Service Provider) option for it to use for WAN/Internet. After configuring the WiSP interface to connect to the strongest AP for the hotel's SSID, I hooked up my laptop to my home SSID and answered the captive portal once. From there all of the rest of my devices jumped on with no problem.
Another feature of using my own router is that I was guaranteed that communication between my iPhone and the Chromecast would be supported. Unfortunately there was one downside to the WiSP interface. It insisted on being configured to connect to only one BSSID which meant if the AP went down it wouldn't roam automatically to a better signal. I've looked into using DD-WRT instead of the built in firmware to get around this, but so far it seems that this particular model is not DD-WRT supported. All in all, my solution worked and I look forward to giving it some more road tests.