New York Marriot Marquis Hotel is located just in Times Square. Is a bit expensive but you can stay in the hearth of NY, also very near from the station.
If you arrive by JFK airport you can hire a car with the Easy Terra Company. You can choose a Pontiac for around 200$ a week with unlimited km.
There are many emblematic places to visit but I think no one can lose The Liberty Statue, Times Square, the Brooklyn Bridge, Central Park and the Empire State.
And like a tourist, I suggest to have dinner at the View Restaurant at Marriot Marquis Hotel, in the It's only revolving restaurant on the top floor of the city