It is really up to you - you can walk (but it is BIG!), take the subway or get a taxi. I recommend picking the sights you want to see and plan to take the Subway - which is cheap and easy. Taxis can be slow in traffic and get expensive quick.
And you will have to take the ferry to Liberty Island, of course! almost 9 years ago
For sightseeing, the best bet are the red double decker buses with the open air upper decks. Check with you hotel concierge for details.
As for getting around the city on your own, the subway system is very inexpensive and efficient. Load up a pass card for each of you and it's a breeze.
Taxis are also fairly decent if you want to stay above ground and enjoy the view along the way. A ride from midtown to most any spot in Manhattan will never be over $20 for the longest distances. You fare will likely be closer to $10.
It's a very safe city, but always to be careful - wallet in front pocket, purse closed and hung across opposite shoulder. Always be aware of everyone around you.
Have fun and enjoy an amazing city. almost 9 years ago
Plan what you want to see, get a good map of the city including the subway system - then walk and catch the subway. Ferry across to liberty and Ellis island, only catch a cab if you really need to!
The movie sites/tv show tours and stuff are great if your into that kind of thing. The pizza tours are also really fun!
Purchase a city pass so your entry into all the big attractions (Empire state, Statue of liberty, rockefeller centre, museums etc) are prepaid. Don't buy tickets from people off the street. They're rip offs and always try to sell you add-ons that you just don't need.
Have a great time - it's an amazing city! almost 9 years ago