Day 1: Ready to feel overwhelmed?
Assuming you fly in today, you might need some time to unpack, freshen up after your arrival and recover from the jetlag, so the itinerary of this first day is very short.
If you have more time (and you like art), you might want to throw in a museum, such as MoMa, the Museum of Modern Art, which is close to the area I'm suggesting next. If shopping is more your thing, you can head to the 15-floor Macy's store where tourists receive a standard 10% discount.
Otherwise, take your time to do whatever you need to do, then head out to Times Square before nightfall and witness the transformation that takes places on Times Square as soon as the dark sets in and all the bright billboards light up. You should also check out some famous stores situated in the area, such as Hersheys, M&M's World and the Disney Store. Fashionista's will love the huge Forever 21 store as well. End the evening American-style with a burger and fries at the popular Shake Shack.
Day 2: Explore upper Manhattan
Head to Jazz at Lincoln center where you take the elevator up for a view over the Central Park area, then walk along the southern edge of Central Park towards the Plaza Hotel, Tiffany & Co, the (ugly) Trump Tower, the Saint Patrick's Cathedral and the Rockefeller Center. On a sunny day, Bryant Park is a lovely spot for lunch where you can picknick at one of the many wooden tables. Otherwise, hit one of the many lunch bars around the park. Make sure to enter the beautiful New York Public Library (and the amazing Rose Main Reading Room) right next to the park. From there you can walk on towards the Chrysler Building and the Grand Terminal.
By the time you've finished this itinerary, it's probably 5-6pm. Depending on the season (and the length of the days), this would be a good time to head back to the Rockefeller Center and take the elevator up to 'Top of The Rock' just before sunset.
If you're hungry (but you cannot be too hungry), you should go to Ellen Stardust's Diner. A waiting line of 1 or 2 hours is not uncommon, but it's worth the wait. You'll be rewarded with a very special dining experience: The waiters sing and dance while serving food.
Day 3: Get high in the park (literally)
Try to pick a sunny day for this itinerary and board the Circle Line Cruise. On this boat ride around Manhattan, you'll get to see the Manhattan skyline from every single perspective and pass super close to the Statue of Liberty. After docking, visit the Intrepid Sea, Air & Space museum that lies right next to it. From here it's a short walk to the Gotham West Market, which I absolutely recommend for lunch. A big further down the road you'll find steps leading to the High Line, an elevated park replacing old rail tracks. If you feel hungry again by the time you leave the 2km long park, you'll find plenty of food options in the Chelsea Market.
Day 4: Sunday is Church Day
In this itinerary, day 4 is a Sunday, meaning time to dress up nicely and go to church. Attending church doesn't have to be boring, especially not in places like The Brooklyn Tabernacle. Their service is one big singing and dancing show, that'll make it hard for you not to join in. After the service, walk back through Brooklyn Park. There's a very popular food stall called Luke's Lobster under the Brooklyn bridge. Check it out if you like seafood sandwiches. Then, cross the Brooklyn Bridge back to Manhattan.
If you'd like to see the Empire State Building, now would be a good time. Contrary to Top of the Rock, you don't need to book a time schedule in advance to visit the Empire State Building. Moreover, it's open until late at night, so you can head there whenever you're ready.
Day 5: Central Park
Don't underestimate the size of Central Park. It's one of the largest parks in America, so take your time to walk around and explore the park. If the weather is nice, pack a picknick and have lunch in the park. Start your walk at the John Lennon memorial (in Strawberry Fields), walk through The Mall and over the Bethesda Terrace. You should also definitely walk over the elegant Bow Bridge. If you have more time, walk on to the little castle Belvedere. (Spoiler: it's not as spectacular as it sounds.) Make sure to take some bread leftovers if you want to feed the squirrels. There's lots of them in Central Park!
On the West border of the park lies the American Museum of Natural history, in which you could also spend a few hours.
After all that walking around, you might enjoy a more relaxed evening. What about a Broadway musical?
Day 6: The southern tip of Manhattan
Walk through Battery Park which is where the early immigrants landed in NY. From here, walk on to Wall Street and make sure to enter the Federall Hall. Visit the Trinity Church and the little graveyard next to it. Also say hi to the Bull of Wall Street. Finally, head to Ground Zero, which is where the old WTC Towers once stood. They have now been replaced by the Freedom Tower and those interested can visit the National September 11 Memorial & Museum. You also really have to enter the World Trade Center Transportation Hub with its futuristic architecture.
If you have more time, you can also visit the Tenement Museum (make sure to book beforehand) and eat a knish at Yonah Schimmelís Knish Bakery in Lower East Side.
A fun evening activity would be going to the movie theatre, especially one like Alamo Drafthouse, where you can have a full meal while watching the movie. Or order their 'trash shake', a milkshake that contains as many calories as three full meals. Afterwards, have a drink in the (creepy) theater bar decorated with faces and foetuses. (Yes, they're fake.)
Day 7: Museum day
You could easily spend an entire day in the MET, as it is really huge. If you're short on time, spend about half a day in the museum, then head to The Cloisters in Fort Tryon Park, a museum governed by the MET specialised in European art. With your entrance ticket of the MET, you can visit The Cloisters for free if you do both on the same day.
This itinerary covers most places you should see when you're visiting New York for the first time. You'll notice that in my detailed blog reports, I deviate from this itinerary, which is because the weather didn't cooperate. Thanks to the extensive subway network, it is quite easy to improvise and cross any part of Manhattan at any time.