It's 20 years since I visited and one of main reasons we were there was for the St Patrick's Day parade (spectacular, long and, in your case, n/a), so I would hesitate to recommend anything*. But just to say that my experience of the city confounded my low expectations of the place: I thoroughly enjoyed it, and the people we spoke to (in the hotel, cafes and tourist places) seemed genuinely friendly and welcoming. I also felt safe there, just wandering around, despite the majority of the NYPD appearing to be preoccupied with taking part in the parade. Not that we strayed too far from Manhattan lower than Central Park.
* apart from, maybe, The Ellis Island Museum, as part of a boat trip.