I bought one of these for my travels http://www.amazon.co.uk/Nexus-Slimport-HDMI-adapter-projector/dp/B00DWGB6CU/ref=sr_1_1?ie=UTF8&qid=1393628870&sr=8-1&keywords=slimport+hdmi works a treat on my Nexus 4 and Nexus 7. On most hotel TVs the AV buttons are locked down. If so try pressing the 0 button on the remote they have provided. Hopefully it will allow rotation through the AV channels.
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