Something along the lines of FTL. A game you can play on iPad while you relax on the couch. No fast action as it doesn't play to the platform's strengths, so it'd likely be turn based and allow for complex and strategical planning. Plenty of random factors and unlockable/collectable content for added replay value.
I'd look for not-so-famous or not-so-well-accepted but somewhat innovative game and add some improvement, changes and additions to it.
Like how Lili came about, and everyone thought the movement controls were unique and innovative, when in fact Brandnew Boy had the same scheme with timed taps for combat similar to timed swipes in Lili. Seems like Lili had the better marketing approach too... so i will look into doing something similar next.
Right now, creating a truly unique experience in gaming is a very difficult thing to achieve. Almost everything has been tried already. Im sure something will surprise us from time to time, but innovating from a tried and true formula seems to be the way to go when just starting out.
Exact-Psience My 2014 Top 10 Games of the Year: Monster Hunter Freedom Unite, Hearthstone, VVVVVV, Battleheart Legacy, Wayward Souls, Bug Heroes 2, Powerpuff Girls Defenders of Townsville, Deep Loot, Monument Valley, Bioshock Honorable Mentions: Traps N Gemstones, Bardbarian, Goblin Sword