I would suggest that you book your airfare at least 30 days in advance. Some of the lowest prices are only available with advanced booking. If all of the low priced seats are fully booked, you may be required to pay much higher fares for last minute bookings. You can check web the airline ticket prices on our web pages for all major airlines. There are also a few discount airlines flying out of NYC, but they may offer limited destinations. Jet Blue has some flights out of LaGuardia in Queens and Southwest offers flights out of MacArthur Airport on Long Island. You will have to check their web pages for pricing information.
There are tours and guides available in Manhattan. I suggest you take the bus tours around Manhattan, Brooklyn and Harlam. The tour bus drivers point out all of the major attractions and describe their features. The busses stop at numerous locations throughout the city, and allow you on and off privleges. You can ride until you see an attraction that interests you, get off the bus to spend some time exploring it, then get on a subequent bus to continue the tour. This is an excellent way to become familiar with the main attractions of the city.