Another East coaster here - Learned to speak in Ontario, grew up in Mass, and much of the rest of my life I’ve lived in NY. I’ve only ever heard “watch” for the verb to describe viewing content on the idiot box.
I’ve used “look at” but only as other posters have mentioned, in the form of troubleshooting to see if I could fix whatever was going wrong with it.
I always say “watch”, although I seldom do watch TV. I worked with a girl once who used to say she liked to “look at” a particular programme. It always sounded odd to me. Watch sounds like the person is doing the action for a continuous period of time. “Look at” sounds a lot briefer so maybe that’s what I really do.
I have never heard someone say that they were looking at the television. I actually didn’t know that was something that people said when talking about viewing a television program. I say “watch” and now will definitely take notice as to what people say.