Here's my personal opinion:

The ONLY place to park in Manhattan is the three-level garage on top of the Port Authority Bus Terminal, entered at 9th Avenue and 41st Street. It's easily accessible almost directly from the Lincoln Tunnel (and even easier on the way out). It's reasonably well-lit and patrolled by real police. It's usually crowded -- also a safety element. It's reasonably priced, something like $15/day last time I used it. And you never really have to drive in the city.

Bruce