You're safer at the Hyatt. NYC is a big place but at the same time a small area. You can get anywhere on the subway, and taxis are surprisingly cheap. A bunch of 5 friends and I visited Manhattan, and we found that it was cheaper for a few of us to climb into cabs together than to ride the subway. We went from Central Park to Ground Zero in a cab rather quickly, and since we went 3 to a cab, it cost us less than the subway. There are lots of tourist books about things to see in NY. Times Square is only one of them. Definitely do Times Square at night. The lights and the projections of ads on the buildings is truly amazing. Protect yourself if you're not used to big, bustling cities. Wear your money and valuables in something safe. Don't flash your cash in public. Watch your credit cards very carefully when they're swiped. If you want to see an amazing sandwich, go to Carnegie deli and bring your camera. The sandwiches are worth taking pictures of. Have a good time.
I myself would prefer to stay closer to Times Square! There is always a lot of action going on there. However, Central Park is a very nice area to see. Make sure you take in some of those restaurants out in New York!