We don't have cable, so I stream Sesame Street on YouTube on the big television - rarely do I whip out the iPhone for YouTube or letting her watch anything there. Sesame Street has served as a means purely for me to get a break and her to enjoy the characters she's come to grow fond of (while also learning fun things!)
I too grew up on Cartoon Network, Nickelodeon, and the early days of Disney, so it was something I really enjoyed (just not until later in life). I still feel like I gave in a bit too early, but desperate times called for desperate measures lol!