Are you familiar with New York City?

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I am looking for some advice on New York City. It is a 5 hour drive from here, and we're thinking of taking the trip there in the Spring, either mid-April or towards the end of May. I've been there twice in my life, the last time being 10 years ago. My husband and children have never been. My oldest is a sports fanatic, so we're thinking of bringing him to Yankee Stadium for his birthday! But since I don't know the city well, I am unsure of where to stay or what to see. I need to know the best neighborhood to get a hotel in, because I don't want to stay in a scary or dangerous neighborhood. Our plans other than the Yankee game are to see the Empire State Building, Statue of Liberty, and Ground Zero of where the twin towers used to stand. We also want to see Times Square. We only plan to stay for 2 days, so that is probably enough to keep us busy, I just want to be sure there isn't anything else that we should definitly see while we're there. Have you ever been to NY city? What was your favorite part about your visit? Do you know the best area to stay in? Something not too expensive, but still very safe?