Rockefeller Center is one of my favorite areas of New York to just walk around and be in. It's not nearly as crowded and tourist-filled as Times Square (though there are plenty of tourists), and it's a place where actual New Yorkers work, eat, shop, and relax. In the spring and summer, the sunken plaza is made into an outdoor cafe with tables and umbrellas, but my favorite time of year to be there is in the winter. That's when the plaza becomes an ice-skating rink, and particularly around Christmas, the entire area is transformed. Most of the time the rink is too crowded to even think about skating, and it's also fairly expensive. Wollman Rink in Central Park is much better for that. But I just like to sit back and look at everything, watch the people. I enjoy getting a mocha from Starbucks and a bagel and sitting at a table inside to watch the ice skaters through the windows. It's less crowded early in the morning, and you can usually watch a private session of skating lessons.
Nearby are also NBC studios, St. Patrick's Cathedral and a number of popular sights and shopping destinations. If you're a tourist, Rockefeller Center is a great way to start your day, and even if you live in New York, it's not a bad way to spend some time in a tourist area without feeling like one.