If you have never been to Manhattan then take one of the tour buses - either GreyLine or BigBus. Once you have been around the city this way, then pick where you would like to go to see on your own and then walk or take the subway or bus.
Advice for first time NYC tourists from a lifelong New Yorker - Don't wander aimlessly looking as if you don't know where you are going. Don't talk to anyone who just comes up to you to "help" you, sell you something, or who seems just too interested in you and your family. Keep your wallet where no one can brush up against you and take it. If anyone wants to hand you something and says "Check it out!", just keep walking - you don't want to check it out - unless you are looking for a different type of a "good time". Mostly, everyone is nice but we have something in NY called "healthy paranoia" - just be aware of your surroundings and who is too close and you will have a nice time.