I go to New York quite a bit with work. It's fucking massive, grubby and absolutely rammed full of bellends. You'll have fun though if your doing the touristy stuff for a few days. Other than that, meh.
As others have said, walk as much as you can, the subways are really handy, but walking gives you every aspect of the city. Brooklyn is one of the strangest places I've ever been to. Extreme wealth to abject poverty living literally next door to each other on some streets. Don't know why but couldn't get my head around the disparity.
Never once felt uneasy/unsafe, even walking (stumbling) about in the middle of the night after a few hours on the piss. There's groups of blokes stood about trying to sell you drugs (at night) but you'll never see so many coppers knocking about.