Top things to see in New York City 

The Lady of Bedloe Island (Source: Alan Strakey)

This is the site that symbolizes NYC. So a visit here and a photo op is a must for every tourist visiting the city. The Statue was gifted by France to the US in honor of their friendship which happened at the time of the French Revolution. It's now considered as the American symbol of freedom. Here's a review extract:

Lightening the torch for World

You can go there either from the New Jersey or from the New York but from either side you will have to take the ferry on Hudson river to reach to Liberty Island. You may want to take a stop at the Ellis Island where the ferry does make the stop. When ferry moves towards Liberty Island and you first gets a glimpse of Statue of Liberty, it would definitely come to your mind, how was this huge structure built? The answer is in the museum which is inside the monument. The monument tickets are limited during the day and are available free of cost. When you book your ticket online make sure to select the monument ticket also.

(Source: TripAdvisor) 

To reach the landmark, you'll need to take a ferry from Battery Park City or New Jersey (NJ). Though admission to the statue is free, you need to purchase tickets for the ferry ride.

Ticket prices: Adults - $12; Senior Citizens (62+) - $10; Children (from 4-12) - $5; Children (3 & below) - free

You can check the latest ticket cost and purchase your tickets online. There will be no need to purchase any tickets if you have availed the New York Pass, which gives you free entry to over 55 NYC attractions, including the Statue of Liberty. Click here for ferry schedules.

Statue of Liberty phone: +1-212-363-3200. Do read these tips for your visit.

The Brooklyn Bridge is now the city's best-known symbol of the age of growth that seized the city during the late 19th century.Visiting the Brooklyn Bridge is one of all-time favorite New York activities. Walk across the bridge and imagine the awe that New Yorkers of that age felt at seeing two boroughs joined by this span. It's still astounding! I am sure you will just love the place.

Brooklyn Bridge II (Source: Ludovic Bertron) 

A visitor says

If you are visiting NY, then take a walk across Brooklyn Bridge.
The walk from Manhattan to Brooklyn across the bridge is great, especially the first half or so.
My husband and I went for a walk here. We crossed the bridge, and got down and wanted to go to Grimaldi's pizza (an ex-colleague of mine had strongly recommended this place to me). Unfortunately it was closed for Easter... This part of Brooklyn is so pretty. There are beautiful gardens once you cross the bridge and enter Brooklyn. And the whole atmosphere over here is so cheerful!
We both thoroughly enjoyed the whole experience (not just the walk across the bridge)

(Source: Tripadvisor) 

Address
cnr Park Row & Ave of the Finest South Street Southport, 10038
Transport
4, 5, 6 to City Hall
Phone
tel, info: 212 484 1200

Times Square is worth a visit if only to witness the distractions that the many many video screens and LED displays provide. Beware of the crowds though, sometimes they can get very very stifling. According to Frommers,

Most of the Broadway theaters are around Times Square, so plan your visit before or after the show you're going to see. For your pre-theater meal, walk 2 blocks west to Ninth Avenue where you'll find a number of relatively inexpensive, good restaurants. If you are with the kids, the Ferris wheel in the Toys "R" Us store makes a visit to Times Square worthwhile.

(Source: Frommer's) 

A Broadway show is highly recommended if you enjoy theater. Visit www.broadway.com for more information on tickets. Also, here is some help from Wikitravel:

New York's Broadway is famous for its many shows, especially musicals. You might want to visit TKTS online, which offers tickets for shows the same night at discounted prices, usually 50% off or visit BroadwayBox.com, or NYTix.com, community sites posting all recent Broadway discounts. TKTS has two offices, one at Times Square with lines often hours long, and a much faster one (sometimes minutes) at South Street Seaport (Corner of John St, just south of Brooklyn Bridge). Note that only cash is accepted at South Street. Show up at opening time for best selection. Tickets to most Broadway shows are also available from the Broadway Concierge and Ticket Center, inside the Times Square Visitor Center.

New York City (Source: Wikitravel) 

Times Square, New York, NY (Source: Jose Oquendo)

As the Financial capital of the world, the Wall Street has seen innumerable fortunes made and lost. (unfortunately more of the latter in the last 2 years) While the U.S. economy may have seen better days, there's little of the doom and gloom feel on wall street, especially outside the bustling New York Stock Exchange which is a nice place to people watch and enjoy the classically designed buildings.

The Charging Bull (Source: Rob Jamieson) 

At the heart of the action is the New York Stock Exchange (NYSE), the world's largest securities trader, where billions of money change hands.

Wall Street Historic District Panorama (Source: Michael Daddino)

A visitor has this to say

My wife and our two boys went on this walk and we thoroughly enjoyed it. There is so much history in this area, and you would never know half of it without our guide. We feel so much more knowledgeble and connected to this fascinating place. The walk is at an easy pace, but it was nice to get in a little exercise while touring the area. I've been able to relate so much of what I learned to my friends and colleagues back home. At the end of our walk, we had a nice lunch at a restaurant recommended by our guide close to the end point of the walk.

(Source: Tripadvisor) 

New York Stock Exchange

Address
8 Broad St
Transport
2, 3, 4, 5 to Wall St, N, R to Rector St
Phone
212-656-5168

What can one say about Central Park? It is not just the lush sprawl of verdant greenery right in the heart of Manhattan; the park has played a strong supporting role in countless dramas and romances.This is a great chance to get in on the magic, stroll on the waters edge together, enjoy an authentic venetian style Gondola ride or take a horse drawn carriage ride for two.

sunset at the rowing pond (Source: b k) 

The Park Zoo and Wildlife Center and the Obelisk are some of the prime attractions within the Park itself and are worth a visit while you're in the area.

830 5th Avenue, NY 10065-7095 | Ph: (212) 360-8236

Open Mon-Sat 9am-6pm

For more information on the Carriage rides click here. Tours vary in length and start at about $165 for a 40 minute tour. (for up to 4 people)

If you're interested in the Gondola rides then you can check out this link. The rate to charter a Gondola is $30 pre half-hour.

New York has some of the finest art museums, and the Metropolitan Museum of Art (also simply called the MET) is one them. The museum comprises of an art collection of more than two million pieces of art and is a must visit when you're in town if you have not already.

Metropolitan Museum of Art (Source: Michael Gray) 

Address: 1000 5th Avenue, New York, NY, United States | Ph: +1 212-535-7710 

Hours:Tue - Thur: 9:30 a.m. - 5:30 p.m. |Fri and Sat: 9:30 a.m.- 9:00 p.m. |Sun: 9:30 a.m-5:30 p.m.
Mon: Closed

Admission:General admission: $20.00 | Senior admission $15.00

Located on the 67th, 69th, and 70th floors of Rockefeller Centre, Top Of The Rocks has an amazing view of Manhattan which can even rival the views from Empire State Building. It was initially opened in 1933 and reopened again in the year 2005. 

Top of the Rock Observation Deck (Source: Smart Destinations) 

This is what a traveler has to say:

I've been to the observation decks at Empire State Building and Top of the Rock (both twice) and I will honestly tell you that if you only have time to do one, go to the Top of the Rock. Same price, better experience. The elevator ride is awesome and the views are fantastic! There are 3 levels at Top of the Rock (only 1 at ESB) and the crowds are smaller. We walked by the ESB on our last trip about 9 PM and the line was round the block! We got straight up on both trips taken TOTR (October and June). You can't see Central Park from ESB, but the full park is able to be viewed from TOTR.

(Source: Rockefeller Center - New York City - Yahoo! Travel) 

You can purchase tickets online through their website here.

Hours: Daily - 8 a.m. to 12 a.m.

Admission: Adult $22

Address: 30 Rockefeller Center New York City, NY

Ph: 212 698 2000