I love Little Italy & Chinatown: they have real character. It's also great fun walking/biking on the Brooklyn Bridge with friends. Generally, SOHO & parts of downtown Manhattan are great. I love Chelsea. Parts of downtown Manhattan like Christopher Street are really gritty, & I used to go there for Halloween parties every year. Places like Wall Street, WTC, WFC are fine, but they don't have any real character. Much like mid-town Manhattan, it's a bit plastic there. Not a fan of Little Korea. Central Park is a bit too commercial as well. I like uptown Manhattan more than midtown as well. I don't know how many people are into museums, but the Guggenheim, National History Museum, Museum of Modern Art, Met are pretty cool too. And Apollo Center & Harlem has got to be one of my favorite places as well (beware: if you're meeting up with a pot dealer there, they have secret cameras there & you can be busted. The safest place to get pot in the city would be in SOHO, at one of the stores).
In the 70s & 80s, the city had real grit: it was almost as if it came out of a **** movie (see Amy Winehouse's videos). People used to sex & orgy each other out. Now it's all cleaned up & commercial.