As a parent you can really trust the BBC for delivering high quality children's programmes in an ad-free enviroment. This website is great and has a lot of games and activities to keep your child busy.
Cbeebies is home to a lot of children's' favourites like Mr Tumble, the Octonauts and In the Night Garden(a toddler classic). Most of the games on Cbeebies can be played on a computer. I havent tested it on tablet devices.
Some Memorable Games:
A fun game where you can draw, paint and also add pictures of your favourite characters.
Help Mr Tumble with this Matching Game
Resources for Parents
I stumbled across this really helpful section in "Something Special" that includes many useful resources for parents, especially those with children with learning difficulties.
Although not as content rich as the PBS website the Cbeebies website provides excellent free material and will keep your children busy for ages. It is also a very useful resource for parents and in general very educational. I like the fact that all this material are advert free.
You can visit the website on www.bbc.co.uk/cbeebies