We visited New York in Fall 2013. This is not the first time we visited the NY area, but this is the first time we (finally) managed to put on our touristic hats and take a few snaps. As time was short - which we guess might be the case for a number of tourists - this post will be about maximizing your coverage of NY wonders in a day rather than a comprehensive description of NY 'sights to see'.
If you are staying on the outskirts of NY, a good starting point is to arrive at the Penn Station (for trains) or the Port Authority bus terminal in NY. Both are within walking distance of the main attractions, such as Times Square, Empire State Building, etc. The traffic conditions are clearly not ideal for driving in NY, esp. not as a tourist. So be prepared for traffic delays if you use the bus. Trains / metro are clearly better in that respect but their stops may not always be the closest to your residence.
The best way to explore NY is to get on a hop-on / hop-off bus tour. Unfortunately, we did not find any offers for a 24hr ticket, so instead had to settle for a Gray Line 48hr (all tours) ticket (link) for $54. Note that you can only buy their vouchers online. Once in NY, you have to go to their office to get the actual tickets. They have an office in the Port Authority bus terminal or you need to walk a few blocks to their main office: 777 8th Avenue.Also remember that while these buses run every 20-30 mins, they are often overcrowded and you might have to wait for half an hour or more to get on a bus from a stop - so take this into account while planning your trip.
Interesting trivia: While NY might seem a jungle of high rises at first sight, it is actually surprisingly easy to navigate. Just remember that all Avenues (Ave.) run North to South, while all Street numbers run East to West.
Statue of Liberty
So you have a bus ticket: A worthy first target would be the Statue of Liberty. The Statue of Liberty needs no introduction and is clearly one of the most recognizable landmarks of the US.
To visit the Status of Liberty, take the downtown loop bus tour and get down at the stop: Statue of Liberty / Ellis Island. From here, you will get ferries that will take you to the island and you can visit the Statue of Liberty up close. However, the (airport like) security checks and huge crowds make it a very time consuming task - which you can ill afford on a 1 day trip.
An alternative is to walk a bit and take the Staten Island Ferry. The ferry connects Manhattan to Staten Island every half an hour or so. The ferry is free and offers close up views of the Statue of Liberty. The plan is to take the ferry to Staten Island and then return to Manhattan - overall approximately 1.30 hrs duration. Remember to ride on the starboard side of the ferry (right side facing the front) from Manhattan and the port side from Staten Island for the best views (to the west) - tip courtesy wikitravel.
The ferry also provides wonderful views of the NY skyline and Manhattan / Brooklyn bridges.
Returning to Manhattan, keep walking back in the direction of Brooklyn bridge. If you took the downtown loop bus tour from the Gray Line main office, you would have encountered the Brooklyn bridge stop during the onward journey - so try to retrace your steps. Walking back a couple of stops also has the advantage that you can visit the World Trade Center (WTC) memorial site and Wall Street Bull in between.
The Brooklyn bridge is one of the oldest suspension bridges in the US, and definitely worth visiting. What is particularly interesting from a touristic point of view is that there is a walkway for pedestrians on the bridge.
The pedestrian walkway is particularly amazing in that you can feel the cars zipping by beneath you. You also get wonderful views of the adjacent Manhattan bridge and NY skyline.
Times Square / Empire State Building / Rockefeller Center
While returning, take the downtown loop bus tour from the Brooklyn bridge stop and get down at the Rockefeller Center stop. From here you can easily walk to the other main attractions, such as Times Square, Empire State Building, or Saks 5th Avenue (for the shopping enthusiasts). Walking is the best way to feel the heart of this pulsating (also very crowded) city surrounded by giant buildings.
No trip to NY would be complete without an ariel view of the skyline, esp. at night. Now you can do this from the top of either Empire State Building or Rockefeller Center. Rockefeller Center is better in the sense that you can get amazing night views of the Empire State Building in all its glory from the top, so we chose the Rockefeller Center - you need to get tickets for the Top of the Rock tour. Beware that tripods are not allowed here, though they seem to allow the table top kind of small tripods, so choose wisely. The Empire State Building Observation Deck, on the other hand, is more recommended for day time views as it offers amazing views of the Brooklyn / Manhattan bridges and Central Park.
Liberty State Park, NJ
Finally, if you are staying in NJ (as we were) and have absolutely no time to visit NY, the best way to get a feel of NY is to visit the Liberty State Park. The park offers close-up views of both the NY skyline and Statue of Liberty, without actually being in NY.