Ok, so everyone already knows the New York City of Times Square, the World Trade Center (both old and new), Central Park and so on. There's also the boutique shopping in SoHo, an "authentic" dinner in Little Italy, and crossing the Brooklyn Bridge.
But what else is there?
Plenty of stuff — for the urban explorer who's prepared to step off the beaten path a little. And venturing into Brooklyn and Queens (and the Bronx), there's even more to discover still. But I will focus on Manhattan here, it being my personal favorite borough despite the recent trendification of much of Brooklyn.
Upper Manhattan: Inwood & Washington Heights
Right at the top of Manhattan, at the uppermost tip starting at around 218th St. and heading down, is a neighborhood called Inwood. Out-of-state transplants moving to NYC are just now starting to discover this area, but tourists not so much. Here, you will find some beautiful parks such as Inwood Hill and Fort Tyron, and just adjacent, numerous bars and restaurants. Along the riverbanks are stunning views of the less famous but equally spectacular bridges (Henry Hudson and Broadway). And also views of The Bronx and New Jersey on the other side of the rivers.
Walking the streets here, I felt a much greater sense of peace and tranquility in contrast to the chaos further south.
The next neighborhood directly below Inwood is Washington Heights, a Latin district where the dominant demographic isn't Mexican or Puerto Rican, but Dominican. The charms of this neighborhood are simply in the day-to-day street life — of authentic Dominican food and bars, markets, music and whatever else. The terrain varies a little here also, with parks and random staircases on hillsides, that offer some picturesque views of the city. During the day, this area is safe enough; although at night you should probably exercise a little more caution.
Washington Heights is fairly large, and the main commercial strip is along Broadway. To the west is Fort Washington Park and to the east, Highbridge Park — which, as with Inwood's parks, offer nice views of New Jersey and the Bronx.
South to Harlem
Continuing southbound, the next neighborhood that follows is Harlem (at this point, you'll want to get on the train, since walking all the way from Inwood to Harlem is quite an effort).
Harlem is quite a large neighborhood and varies a lot in terms of demographics and social class. There is still the Harlem of old, with street gangs and violence and a degree of poverty. And there's also the newly gentrified Harlem — which in my opinion is still at a level of "good" gentrification (local businesses and shops outnumber chain stores).
Some might dispute this opinion, though; there is an uneasy kind of truce that exists between the traditional African-American residents and the newer, mostly out-of-state college-graduate transplants moving into the area.
I'll focus on this gentrified area, which begins more or less around the 125th St. station of the A/B/C/D lines (at the corner of 125th St. and St Nicholas Ave.), and continues southeast along St. Nicholas Ave. until it meets Frederick Douglass Blvd. The main strip of nice restaurants and cafes and bars in this section of Harlem includes Mess Hall/Double Dutch, twin establishments run by the same ownership (one a nighttime bar and the other a daytime/evening cafe).
West of here, you'll find Morningside Park, a pleasant spot to chill out on the benches under the trees with a locally bought NY-style deli sandwich. Ascending the stairs inside this park towards Columbia University, take in a beautiful view of the neighborhood and city below.
More off-the-beaten-path NYC
Back on Frederick Douglass Blvd and continuing south to 110th St., you hit Central Park. This upper section is a little less touristy than the midtown sections and is beautiful regardless of the season: radiant sunshine in the spring, shady trees offering a respite from the heat in the summer, colorful foliage in the fall. Or, sip a hot coffee and enjoy the snow in the winter.
There are plenty of other off-the-beaten path neighborhoods worth exploring in Manhattan, and even more in the outer boroughs, but that's another article.
The material here will easily fill a day. And if you still have time to spare, there's East Harlem (obviously, east of Harlem), which houses a Latin population — mostly Puerto Rican but also Mexican — Morningside Heights, situated west of the magnificent and prestigious Columbia University, and below this (geographically speaking) the well-heeled Upper West Side.