I use an Ipad with AVPlayerHD loaded up with everything I want to watch. No need to worry about wifi or stuffing around with getting access to the HDMI port. If I have wifi, then I can watch Netflix on it as well.
It is an expensive option if you otherwise wouldn't buy a tablet though, so if that's the case, then yeah, I reckon give a chromecast a go - it's cheap enough that if you don't use it, you haven't lost much and can probably use it at home anyway.
You will need to set it up to connect the a new wireless network every time though, which might be a pain/not possible depending on the setup of the hotel network. I also reckon I'd leave about 1 per week behind in the room.