Hire bikes and cycle round Central Park, then go for a drink in the Tavern on The Green. Go to Marriott Marquis Hotel in Times Square and go up the futuristic pod lifts to the revolving restauarant. Might have to queue. They had a very reasonably priced buffet as well. The best thing I did was stand on top of the Twin Towers and look down on it all. Pleased to have done it but still so sad I can't do it again. It's great to get up early, which you will, becasue of adrenalin and jet lag ,especially when the light is good and just wander around. Stand in the middle of Grand Central Station. Visit Madison Square Garden for an interesting tour. Carnegies (?) Deli Diners of any type. Take the boat across the Hudson and the train back, or vice versa, for a different perspective across Manhattan. And after all these suggestions, go for a month!