If I must drive to visit NYC, is there a safe place to leave my car
somewhere on the western outskirts and have public tranportation into
and out of the Manhattan area? I do not want to be much more than an
hour away and would consider an airport if that is possible.

Hello and thank you for your question.

Most convenient and most expensive, you could drive into Manhattan via
the Lincoln Tunnel and leave your car at
CENTRAL PARKING formerly
KINNEY SYSTEM 
PORT AUTHORITY GARAGE
Telephone number:
212-502-2341
Open from 6 am to 1 am daily 
7 days a week
Rates:
(Both weekday and weekend)
New Parking rates effective April 1, 2005 
(taxes included)
up to 1 hour $15.00 
up to 2 hours $17.00 
up to 12 hours $22.00 
up to 24 hours $26.00 
Early Bird $18.00 
(before 6:30 AM) 
http://www.panynj.gov/tbt/pabmain.HTM

Cheaper and more what you had in mind, you should leave your car at
one of the PATH stations in New Jersy and take the PATH train into
Manhattan.
All of your choices are described in this handy booklet - - personally
I'd park at one of the Kinney lots in Jersey City since that's the
nearest and easiest ride in:
PATH Parking Guide
http://www.panynj.gov/CommutingTravel/path/pdfs/NEW_ParkingGuide.pdf

I'm not listing Newark Airport as a choice, because I once had my car
stolen there (from a park-and-fly hotel parking lot)!

Search terms used:
"new jersey" "port authority" parking
"new jersey" "path train"  parking

Thanks again for letting use help!

Google Answers Researcher
Richard-ga

There are two major airports in the Manhattan vicinity- John F.
Kennedy & LaGuardia. All large airports have long-term parking at a
few dollars per day, and there's no particular reason that you
couldn't just park your car in such a lot and take a taxi to your
hotel in the city. I stayed in New York for a few days just recently
(I flew into LaGuardia), and the cost of a taxi ride could cost in the
neighborhood of about $50. (It could cost somewhat less, but fifty
bucks is a realistic exectation.)

You ask about western outskirts.  LaGauardia and JFK airports are on
Long Island, a goodly drive still if you are coming from the west.
I suggest Newark Airport in New Jersey:

http://gonyc.about.com/cs/airlinesairports/a/getto_ewr.htm
http://www.airwise.com/airports/us/EWR/EWRpark_costs.html

There may be cheaper safe parking in Newark, itself, also a cheap
commute to Manhattan.

Park at Metropark Train Station in Iselin NJ (just off the Garden
State Parkway) and train into the city.

myoarin-ga, by Newark do you mean the carjacking capital of the U.S.? 
Perhaps Ironbound is safe (look for Portuguese and Brazilian flags),
but anything west of Newark Penn Station is to be avoided.