My wife swears by using a FireStick. It was miserable due to hotel captive wifi portals often failing to work properly with the browser of the FS, and even when it does work, typing your name/room number is miserable on a TV.. Adding a travel router to the mix allows you to auth via phone/laptop, which makes things a whole lot nicer.
Unlike the sibling, I've never encountered a hotel with all ports blocked. But I have encountered hotels where there is no way to choose other ports. In that case, I've just unplugged their STB and plugged my FS in.
I haven't tried this on iPhone yet, but on android you can share Wi-Fi connection. Many times I've connected phone to hotel Wi-Fi and then chromecast to my phone.
Sadly, we're both on iPhone and you cannot share Wi-Fi like that on iPhone :(
This was a bummer just the other day where my iPhone somehow (and I still don't know how) auto-signed into an amazingly fast wifi AP managed by my cell provider, but I was stuck working on crappy guest wifi on my laptop and could not get the laptop onto the better wifi.
Unlike the sibling, I've never encountered a hotel with all ports blocked. But I have encountered hotels where there is no way to choose other ports. In that case, I've just unplugged their STB and plugged my FS in.