OK, I have streaming apps installed on iPad but in case you want to watch on big screen. Though many hotels make it difficult or impossible to reach HDMI ports.
Issues to overcome:
1. Hotel wifi which require logging in each session, using some kind of browser-based setup. Some people take traveling routers. Alternatively, get a lot of mobile data and hotspot from your phone or iPad, because you have a good chance of getting much faster speeds.
2. Region restrictions from streaming services - VPN can be run on iPad and phones. But are there VPN apps you can run on Apple TV or the Chromecast with Google TV, which is a $50 dongle on which you install apps? Can you run NordVPN or one of the other popular VPN service apps? Or even something like OpenVPN, if you want to set up a private VPN server?
Never really tested it but maybe I run VPN on my iPhone or iPad and then hotspot the connection to the streaming device, which should inherit the VPN'd IP address?
I always travel with a Roku Streaming Stick+ and a GL.Inet travel router. I have both their Mango (GL-MT300N-V2) and Slate (GL-AR750S-Ext) routers. Both are USB powered.
The key advantage to these particular travel routers is that they are designed for this exact use. Unlike any other travel router I've used, these will display a list of available networks BUT also remember ones you've already connected to, just like a cell phone. If you travel to the same hotels often, or even the same chain often, you'll find it'll connect automatically. These routers also support all of the major VPN services on the router itself. The Gl.Inet routers also have a physical switch on the side of them which will turn the VPN on/off. No apps needed.
So, when I go to a hotel, it works like this:
1) Plug in the travel router to power. Takes about 30 seconds, so I plop it on the desk first and continue unpacking my other electronics.
2) Log in to the router with my phone, tablet, or laptop.
3) Connect the router to the hotel's WiFi or hardwire
4) Use the phone, laptop, or tablet to sign on the hotel's log-in screen. You only have to do this once, since the hotel sees the router as a single computer and can't see all of the other devices you have connected to it.
5) Enjoy. All of my devices are already connected to my travel router. No need to sign all of them in again. Optionally, flip the switch on the side of the router to turn on your VPN. I just use my office's VPN most of the time, although I also have my home VPN in there if need be.
As far as hotel TVs being difficult, I've not run into a single TV I couldn't connect my Roku to in the past 4+ years in any country I've been in. For most of them, make sure the TV is turned off. Unplug the HDMI cable, unplug the RJ-11 (telephone-style) cord from the cable box to the TV. Turn on the TV and it acts like a normal TV. I even can use the Roku's remote to control power and volume.
As far as buying these things, on the Roku, wait until Thanksgiving; you can pick them up for $30 each.. the voice remote alone sells for $20. On the Gl.Inet routers, the Mango does a decent job for what it is. If you're wanting top-notch VPN performance, get the Slate as it has much more horsepower than the Mango. Never really been an issue with me, but I'm a relatively light user.