I've played a ton of mystery games on my iPad, so many that I could've sworn I already wrote this post. The three games below are my favorites. They're all available on iOS and they're noirish and fun.
Detective Grimoire: Secret of the Swamp is stylish and a bit silly. It reminds me of Broken Age -- a colorful world, a distinctive look, very polished. I'm not the only one to compare the two games -- this reviewer calls Grimoire the antidote to BA!
Puzzle Agent and its sequel (Puzzle Agent 2, Electric Boogaloo, just kidding it's Puzzle Agent 2) have goofy jokes and a cartoonish design. Yes, as with most point-and-clicks, you have to run back and forth between locations and talk to characters multiple times, but in this game it's not annoying, somehow.
Agent A has a cool, retro-futuristic feel, like the Jetsons or old Bugs Bunny cartoons. I love the fact that both Agent A and the villain, Ruby la Rouge, are women. I also love that the game advertises itself as playable on shoe phones.