I tried it once but have given up on it. The biggest problem is getting it connected to hotel Wifi networks that require a browser-based login (which is most of them). There are ways around that (e.g. using a travel router), but it's a hassle.
If you don't need iTunes content, a Roku 2 or Roku stick might be the best solution. With the latest OS update they got the "hotel and dorm connect" feature for browser-based logins. The stick is obviously more compact, but the 2 has an Ethernet port which sometimes comes in handy.
Personally, I mostly just connect my iPhone or iPad to the hotel TV using the Lightning/HDMI adapter these days.
I just chuck mine into my bag with my airport express. Dont bother with cases or anything, i just put them between some shirts to stop them from flying around or scratching, no moveable parts in them so unlikely that they will get damaged
I will take my 3rd gen instead of the 4th gen because it is thinner and easier to fit in my backpack. I will probably end up leaving the 4 at home most of the time. When I take the three, I stick it in an AmazonBasics Universal Travel Case, but I am not sure if the 4th gen will fit ( I haven't tried it, though).
I use a merino wool ATV cozy, a set of silicon plugs for the ports, a neoprene sleeve and breath mint tin for the remote, and keep it all in a Zero Halliburton custom molded aluminum briefcase, with handcuff lock.
I travel a LOT and bring my Airport Express, ATV3 and ROKU Stick with me. Anytime my hotel room has an ethernet port I will use my Airport Express instead of the hotel WiFi, so much more stable, I will also run an ethernet to the ATV3. Most of my electronics either go in the Pelican cases with my clothes, or in my camera backpack when on the move.
To get around the hotel login pages I just spoof the MAC address on my laptop to match the ATV3/ROKU address, then log them in, and then change the laptop back to it's original MAC address. It's a simple copy/paste command in terminal to do this. It's not worth the hassle if the hotel makes you login every few hours though.