I live in North White Plains in the middle of lower Westchester County about 15-20 miles north of Manhattan. Not sure what would be the best way of biking into the city, I'm a 20 yr old white kid so going through the south bronx on my own is a little uh... I don't want to get my ass kicked if I end up in the wrong neighborhood. Anyone from around here know what I am talking about? I only have a few years road biking experience so someone with a little more navagating ability would help, I only know how to get to a lot of places with highways. Oh yeah if you hate SUVs stay out of Westchester god damn Soccer moms.
I wouldn't be too worried... the south bronx is really not unsafe during the day, just stick to the main roads or the roads on the NYC bicycle map with designated lanes. The Bronx itself is not a bad place, it is full of plenty of great biking opportunities and I find the people to be very nice.
As an alternative, you can get to the city through Riverdale/Spuyten Duyvil and cross the Henry Hudson or Broadway Bridge into northern Manhattan. This is not a flat area though. From there, just ride south on Seaman, turn on Dyckman (ha) and then you'll be on the Hudson River Greenway which'll take you nonstop to midtown, Greenwich Village or Ground Zero.
also, on weekends i believe, the Bronx River Parkway, which goes right through White Plains, is closed to road traffic and is a bicycle and pedestrian only road! a perfect time to head down to the city would be to take the bronx river parkway down to northeast bronx, the pelham parkway, and then down through hunts point down to spanish harlem!