DS watches cartoons while he eats his breakfast (usually Cat in the Hat) and he loves Elmo. I love Elmo too because he gives me time to clean up, make supper etc without DS in my feet. He doesn't care for anyother shows on TV. We travel a lot (to see family) and if I don't want him to fall asleep in the car (not long enough for a decent nap), we will put Elmo on the iPad for him.
As far as other screen time, he also loves to look at pictures on the computer. We do this a lot because we don't have any family that lives close to us and want him to know who they are (if that makes sense). We also watch laughing baby videos on youtube because they make us both laugh hysterically. All of this stuff is done with me.
Long story short, he watches 1 hr of TV and has probably 30-60mins of screen time 4 out of 7 days.