Kim, if you can you *must* go to Katz's Deli on the lower East Side. It is the quintessential NY Jewish deli and has the best pastrami anywhere. The sandwiches are enormous! A number of movies have been filmed there, including the famous "When Harry Met Sally" restaurant scene
You cannot go wrong with seeing a Broadway show or visiting any of the major museums, such as the Met or Natural History. Just walking down 5th Avenue and window-shopping is fun. Not sure if there is still skating at Rockefeller Center in March, but that is something I enjoyed as a child. There are other skating venues in the city as well.
Depending how long you are staying, you will want to pick one or two parts of the city to explore. It takes time to get around no matter how you go, so plan your days according to the proximity of the attractions to each other.