PBS Kids is such a fun website! I go on it myself and I'm 10! You can follow your favorite characters from T.V and play educational games with them! I don't see why not 2 year olds can't play. That is one of the biggest times where they need to LEARN. Go PBS kids!
I've been on it loads of times and have never seen a problem about it! It's great for younger kids. (And I still watch a lot of the shows! For example, Fetch, Wild Krats and Wordgirl)