I love my game apps, and they are all appropriate for kids. They're puzzles, and they keep my brain active and engaged. I actually use them to combat my depression sometimes, they keep me from ruminating. These are the ones I play most often:
Best Fiends- a matching game, it starts out really simply so even a child as young as yours can learn it quickly. It does get progressively difficult, though, too. (This is true of all the games I mention here.) You can choose to spend a bit of money ($2-5) to earn more turns in a game, etc... but you don't have to pay to play if you don't want to. The Fiends are adorable, and the company donates to charities that help eradicate Malaria around the world (which is why I don't mind spending a few bucks with them every month). They have an active facebook page if you want to check it out. I did not like the second version of the game, it's basically just repeatedly tapping on the screen with little strategy, but younger kids seem to like it more.
Angry Birds - any of them, and there are a lot to choose from. I especially like Angry Birds Pop and Angry Birds 2. I liked the Stella version, too.
Nibblers - another matching game, this one is made by the creators of Angry Birds (Rovio) and is a bunch of fun with really cute characters.
Panda Pop - similar to AB Pop, but you're freeing baby pandas instead of dropping pigs.
p.s.
If you get stuck on any level of any of these games, the solutions are usually posted on youtube, especially handy for games that let you pick the "players" for each level (like Best Fiends).
