I am not a native one... but I can call myself a New Yorker having lived there long enough
I find Manhattan pretty safe but again nothing to compare with anything in Switzerland.*
Manhattan is very diverse and changes from block to block. But this is again the beauty of it. Depends on your budget and your 'likes' I'm sure there is something that fits you there.
As you are screening your options you can pm me and I will give you any feedback I might have.
* I'm still finding myself amused with the parked bicycles outside Luzern's train station. In NYC the 100m pole with parked bicycles would have been skinned in seconds!