Monument Valley is amazing but short. I got it on sale for a dollar though, and it was certainly worth every penny. ($$$)
Leo's Fortune is a nice, simple, beautiful platformer that works fantastic on a touchscreen.($$$)
Bloons TD 5 is simply addicting yet somewhat strategic.($$$)
Hearthstone is Hearthstone. Proven good, yet could become a money sink. (Freemium)
Peggle Blast is a fantastic FREE game that you can progress through with short bursts of play. Most casual on this list and the one I most recommend. (Unnecessary micro-transactions)
Finally, a more obscure game, First Strike 1.2. Nuclear war simulation/strategy game. Take a lot of pre-planning, lots of fun. ($$$)
($$$) = costs money
Hope I was of assistance!