I've had this idea for a game for a long time, but because I don't ever see myself making it, I'll pass it on to you.
The premise of the game is that you play as a guy fighting zombies, paired with music. The user will pick a song from his/her music library, and the game will use an algorithm based on beats or pitch or something, and will spawn in zombies of ramping difficulty, and as the song goes on, it will get more difficult. The player would presumably be able to get powerups and make money per zombie kill, to buy new weapons and cosmetic items for his/her character.
Monetizing the game is as simple as providing some original music to play along with, and the ability to buy cosmetic items/coins.
I believe this formula could work pretty well because the player can sit down, and play a level on a bus ride, car ride, etc. which makes it something they can pick up and play pretty easily. It also allows them to experience their music in a new way, and the fact that music is involved will make them want to keep playing to listen to all their songs in the game. You draw players in with the initial concept, and keep them playing and making in app purchases.