Google ChromeCast and TV in Europe..

I don't have a clue what hookups your tv has. Generally the same names are made similarly, power and frequency dependent, and some will have HDMI connectors, some will have USB, some will have RCA, old ones might have SCART.

Maybe you can reach them, maybe not. Many TVs are mounted close to the wall and connectors are not possible to reach. Some may have then reachable but non-functional.

Some hotels have smart TVs where you can cast your phone or laptop. Many don't. Be sure you understand mirror cast.

Probably some American tvs are like that too?

Also - unlike the USA - Europe is not one country where everything is the same but the colour of the license plates. Europe reaches from Russia to the Canaries, from Finland to Gibraltar.

Thank you so much, I'll have to think about how much tech stuff to travel with!

Another thing to consider is whether whatever you want to watch is geo-restricted. Some programs-especially live sports-are. So even though you are using your presumably US Google Chromecast account the content provider will know you are using a European IP address.

==>"Some hotels have smart TVs where you can cast your phone or laptop. Many don't. Be sure you understand mirror cast."<==

That's all I did last time in the UK was to use the "smart view" feature on my Samsung tablet & mobile to cast to the room's tv.