Oh I love this thread! Ok, on my iPhone I have about 3 pages of apps so I'll try to list the best ones haha
-"Mini Golf" -"Cube Runner"
-"Crash Kart Bandicoot" -"Expando"
-"Labyrinth" -"Diner Dash"
-"BJ Run Lite" (so addicting!) -"Papi Jump"
-"reMovem Free" -"Tap Defense"
-"TanZen" (highly addicting as well) -"ShakeSpell"
-"Hanoi" -"Stick Wars"
-"Who Wants to be a Millionaire" -"Lemonade Tycoon"
As you can see, I spend WAY too much time on my phone

hahaha
Most of these games kept me occupied when I was hit by a car and when I had shoulder surgery, so my guess is they should keep you occupied as well. I hope everything goes great and that you have a fast recovery!