Hi, Becky. I live in Manhattan - thanks for planning a trip to come visit us.
What you want to do with your "time off" from the tour guide depends on you and your interests. You can see from the other posts that the list of activities is endless.
I imagine your tour includes a stop at many of the main attractions: Times Square, Chinatown, Empire State Building etc., so perhaps you will want something more off the beaten path? The best local periodicals to check out are Time Out New York and The Village Voice - it's best to get them both in hard copy when you arrive, but if you want a preview, both have web sites which carry some of the features and recommendations.
If there's an area of interest (museums, theater, music, rock-climbing, shopping, bird watching etc.), let me know and I will make some recommendations. Otherwise, all I can add to the above posts is to advise you to be sure to keep your wallet in your front pocket, never your back. It's not a dangerous city, but pick-pockets love to target folks at the holiday time...