FraAng, did you personally get a ticket? That seems a bit for fetched for a cop to nail you for that, you could probably fight your way out of that.
I have never had tourist issues on the path at rush hour times.
My one big suggestion is ride on the left side of the lane. On one way streets in NYC (wider than 40 ft- I do it on all streets) it is legal to ride on either side. The poster who mentions tapping cars that are cutting you off, I agree, the driver is right there for you to, um, "interact with" etc. I also rarely get cut off (no right [left] hook).

I feel two issues matter in determining your safety, one, your gender, (sorry) and two, your speed. My girl rides from Columbia all the way down town, often after 8 or 9p she does not ride the path from 59th to about 72nd where there is a lack of lighting it is all torn up due to construction. If you are a guy, I would say you have less to worry about riding around in general. I ride everywhere at all hours and essentially do not worry, there may be a times in deep Brooklyn that I won't take people to task for being stupid and just accept their driving offense.

First avenue is a fast ride, on the left, if you take the lane, you control the turning traffic, and can get uptown rather quick. There is less double parking and if you have already got your self moving 17-18mph you can get swept in the draft and literally glide along at 25-27mph. If you look at other conversations on the Forum about taking the lane, I think you will feel much safer with traffic. I do find that you need to be moving faster than maybe 15mph or appear to be at least working hard, to not have some jackass pass you just to make a point.