The BBC News mobile app is a good example. Each article is predictably laid out. There are no ads. Nothing happens if you accidentally click the photos while scrolling. Give it a try!
I've used it as my main source of getting news from back home. Ignoring the quality of the editing (I spot a spelling or obvious grammar mistake almost daily), the app is decent.
It's straightforward. I can pick the categories I want. It just gives you the top X articles per category, nothing more. Doesn't link you elsewhere. One headline, one thumbnail image, sometimes 1 image embedded in the article. There's are very few buttons to be confused by. One of them is font size. I'd say it's pretty grandma-friendly!
This was true until the recent update - now there are massive great images and you have to scroll around an infinite canvas-style arrangement before you can even find the article you're looking for. Fails the grandma test immediately.