Looking for a site that is super easy to use. Then play at NickJr.com. When my son was 2 years old, he was using this site without instruction. It's almost error proof -- he was clear how to get to Blues Clues and even if he went to another area he could get back himself. Even if he couldn't read the navigation.
Here he is at 3 years old.
He's 4 now, and using other sites such as Kimpossible and SpyKids, but I think NickJr was one of the first to make a site easy enough for a 2 year old to use.
If you're thinking of making your sites easy to use, take a lesson from these kids sites -- big buttons, less is more, logical navigation, reading not required.