I had the same problem as you. Wanted to stream to my livingroom TV from my PC but didn't want to run an HDMI cable across the whole apartment.
I went with the Chromecast approach. I use Plex as a server on my PC and stream to my TV through the Chromecast (which has full Plex support).
It's working great for the most part. Picture is crystal clear with no bitrate issues and full 1080p resolution. The reason I said "for the most part" is because, sometimes, I get buffering issues. The Chromecast does not have any ethernet inputs, it's WiFi only which makes it a little bit unstable at times. Honsetly, it's very rare that I get buffering issues and it can actually be the WiFi conditions in my apartment that are causing these issues, but it is very annoying when it happens.
Obviously wired solutions are better for these types of things (be it HDMI or Ethernet), but I still find the Chromecast a viable solution and also the cheapest.