Grand Central Station is really stunning, if you're lucky enough to catch a train from one of the 47 platforms (I think making it one of the largest in the world), you'll feel like you've stepped back in time. If you aren't catching a train, you should still stop in for a look at this ridiculously majestic building with a turquoise and gold ceiling. Tons of trains to all over the place leave from here, if you're up for a day trip I highly recommend catching a train up to the Dia Beacon Museum in Beacon, NY. It's a beautiful, 80 minute train ride and a great day-trip from the city. Catch any train upstate for that matter and enjoy the scenery!
There's also a food market inside selling tons of lunch options. It's pretty packed at lunchtime but I got some Vietnamese rolls (curried shrimp and blackened cod) for $3 each...and cheap meals in NY are hard to come by!