Hello Mojo,
I think it's great that you've decided to spin around NYC on your bike. You will find that it is by far the best way to see a whole bunch of stuff at once. Here is an attemt to answer your questions:
1. The Department of Transportation recenty released a new up-to-date NYC bike map. They've come a long way in recent years in terms of painting new lanes and building new paths.
Here is a link to the map. Just so you know, the Javits Center is right on Manhattan's premiere bike facility, the Hudson River Greenway. This is a MUP that runs up the Hudson River all the way from the Battery to Inwood Hill Park.
2. Sounds like a pretty good plan. Central Park has great riding. I would recommend crossing one of the East River bridges, particularly the Brooklyn Bridge if you've never done that before. It can be a little crowded, but the experience is a lot of fun. Once you're in Brooklyn, you can go down Fulton Street and check out the now-under-construction Brooklyn Bridge Park, which I think is neat.
3. The George Washington Bridge does indeed have ped and bike access. The entrance is on 178th Street in Washington Heights. I believe that you're actually not supposed to take pictures on the bridge, but I don't think this is strictly enforced.
4. The idea that there are neighborhoods that are so bad that you're in danger of being the victim of a random attack is an unfortunate remnant of the "bad old days." Please let your wife know that NYC has the lowest crime rate of any large city in the U.S. Random muggings on the street, especially in Manhattan, are so rare that you shouldn't worry. The only real danger is collisions, but keep alert and you'll be fine.
I hope that this answers your questions. Have fun riding!