Local Attractions

• Manhattan: One of the financial and cultural centers of the world. 'Nuff said. It's about 45 minutes away on a commuter train (about $9 round trip). You can also drive there, but it'll take longer and cost more (between tolls, parking, and therapy) than the train. The train goes to Penn Station, from whence you can take the subway, bus, or taxi to anything else in Manhattan.
• The rest of New York City: Contrary to popular belief, Manhattan is actually only a small fraction of New York City. The boroughs of Brooklyn, Queens, the Bronx, and Staten Island have their share of tourist attractions, just not packed together quite as densely as those in Manhattan. You can get to many of these things by public transit, but not as easily as you can get around Manhattan.
• Long Island: Long Island is largely New York City suburbs, and has the sorts of shopping malls found in suburbs everywhere; one such, Roosevelt Field (where Lindbergh started his flight to Europe), is about two miles east of the Adelphi campus. Long Island also has lots of beaches and a number of historic mansions from the 1880's-1920's, as well as other historic sites from its 350 years of European settlement. To get to most of these things, you'll need a car.