Upvote:4
Here is the short story. The Los Angeles River in downtown LA is really not visitable.
Here is the long story. There are portions that are very visitable. Those are just not the ones you see in movies.
http://lariver.org/blog/explore-la-river is a good resource for what is available. The picture at the top of the site (4/3/2019) is no where near downtown LA. I think it is farther north in Glendale.
If I wanted to see the LA River and I was in downtown, I would take the Metro Gold Line and get off at Pico / Aliso. There is a good pizza place there, Pergatory Pizza. It is a pleasant walk over the river. Downtown's building are in the background. It is a good use 1/2 hour.