The Bronx is called Arson City because apartment buildings kept mysteriously getting set on fire. Lots of apartments. The type with needle-shooting, 5-minute whoring occupants. "Weird" is not the operative word here; over 80% of the Bronx qualifies as an urban war zone. Also as a white girl, you're dead meat. Harlem, on the other hand, is being re-gentrified although the process is ongoing and definitely not done; however, not near anything else you'll be going to.

NY Chinatown I think is bigger than the one in SF. Great place to eat. Chinatown, Little Italy, Greenwich Village and Soho are all within walking distance of each other, if you like to walk. Otherwise you can hop a subway. If you have the time (and I was planning your itinerary) I'd do Statue of Liberty/ Ellis Island one day with dinner in Chinatown; Soho, Greenwich Village and Midtown (Rockefeller center, etc.) another day; and the big museums are a full day unto themselves. Most mid-to- uptown museums border Central Park. Shopping is everywhere.