Agreed, you can use Chromecast if your TV has a USB port. It works like a charm and is very cheap.
If it has an HDMI port. (It even has a short HDMI extension cable, in case you can't fit the Chromecast itself in the right position to plug it in to the TV. The USB port is just to power it, and it comes with a power wallwart and a pretty decent length power cable if the TV has no USB port.
As far as streaming, I've never noticed any problems. It takes a while for it to update when you first plug it in, a portrait screen orientation looks funny on a 16:9 screen and you have to run the
Chromecast app if you want to mirror (they call it 'cast') the screen, so you can see any app on the TV. Otherwise only Chromecast-aware apps like Chrome and Youtube (and Firefox sort of) and a few others will work. (The app is free.) Best Buy should still have them for $25. It's worth it if you use it. (
Chromecast mirroring has a list of phones the app works on so far, and instructions on where to press what to get your phone casting. The Note 3 is listed, so the Note 4 should work also. And Best Buy has a liberal return policy if it doesn't work with your phone. I think you have until January 15th to return things bought until Christmas. I know it's January 15th - I don't know when the cutoff is, but any sales associate can tell you. And you can't miss them - they have them piled up like Christmas decorations all over the computer department and at the Geek Squad desk.)