The Chromecast should work fine. I’ve used it in various hotels and in all but one, it’s been fine. The only hotel I had a problem with was due to the hotel policy of only allowing one wifi connection per room.
You should be able to set up your chromecast from your tablet or phone once that is on the wifi.
Don’t forget that anyone else on the network can stream things to your Chromecast once it’s on the hotel’s wifi.