New York is really easy to get around. The subway is fast, cheap and reliable, but walking is also recommended. If you are looking for somewhere specific - grab a cab! Most drivers are really friendly and you often get a gem of knowledge or quirky local anecdote.
In my opinion, the best way to see New York is on foot. If you get a map and mark on all the major things you'd like to see, you'll find that a lot of them clump together in areas of the city. Choose to do one or two of these areas a day and explore on foot.
There is a lot to see thats not in tourist guides - beautiful buildings, gorgeous parks, interesting art work, commemorative plaques with interesting stories and the favourite local shops and restaurants. There is always something happening in New York City - so you never know what you might stumble across.
If you don't feel comfortable about walking around yourself get in touch with the 'Big Apple Greeters'. They are a free tour service, who arrange for a local person to come and show you around! Highly recommended!