I have watched a few Studio Ghibli movies, and they have been very fun to watch! I sadly only have Hulu, YouTube or if there is a free site where you don't need an account, but I will try to check the animes out! (When I get back. On the forums right before I need to go.)
Also, I used to watch Sonic X a SUPER long time ago before I even really knew it was an anime. I would eat McDonalds breakfast, sit in front of the TV and watch it even though I barely knew the plot or what was going on.
Edit because I needed to add more:
A lot of "child friendly" animes can also seem TOO child friendly, almost like a kid's cartoon. But I guess it is sort of? I've also found another (very short) anime called Nyanko Days. It seems to be pretty child friendly, only one "inappropriate" joke at the very end of an episode, and it's not showing nudity or anything.