I've never tried a Fire Stick, but I've tried Chromecast with Google TV (the newer one with the remote) and a few different Rokus. I've never had luck with the Chromecast, at either Hilton or Marriott properties. It never knows how to handle the captive wifi portal. Roku on the other hand works almost every time, so that's what I use when I travel (even though I prefer Chromecast at home).

I've tried using a travel router to bypass it, but in my experience it's usually more hassle than it's worth, and doesn't always work without a bunch of tinkering. Unless you're lucky enough to get a room with a working ethernet jack (properties from the early 2000s are most likely to have that I'd estimate, and seems more common at places like Homewood Suites). I'd rather just use the Roku and the regular wifi.

EDIT: 2024 Update, Fire Sticks also work well at Hiltons for me, they're able to handle the captive wifi portals in my experience. I've switched from Roku to Fire Stick in my hotel bag because Fire TV has more apps like Twitch, Channels DVR, and SmartTube. I guess I haven't had the chance to try at other hotel chains besides Hilton since switching, but the wifi setup is pretty similar at chain hotels so I imagine it will work at other chains too (like Roku does).