The problem with not using a travel router or a personal hotspot, either from your computer or phone is that anyone can broadcast to your Chromecast who is -also- on that network. Of course this is given AP isolation is off, which is necessary anyway. It might be a small problem, but it is still not ideal.
As apperault writes, using his computer as a hotspot works well, but that relies on you having a ethernet port to then use your wifi as a hotspot, which you should just use a travel router in that case. If you do not have ethernet, use your wifi, and share your internet with your ethernet port which outputs to the travel router. So you never have to change your configuration for the Chromecast, or other devices.