Outside of the seemingly chaotic Times Square or somewhat tranquil Central Park, you have the obvious choices of visiting Lady Liberty/Ellis Island (highly recommended), or checking out the progress at ground zero. Little Italy is nice to get some grub at during the evenings if the weather is nice and you can walk around, or use Yelp/UrbanSpoon to check out ratings for different cuisine in various neighborhoods. Around the SoHo area you can find a number of boutique shops varying from jewelery/clothing to house decorations. The museum of natural history is a good choice as well, or one of the many smaller museums on the west side of central park. That's enough to keep anyone occupied for a weekend or two at least.