KathrineAM, You may think that driving into NYC would save you money and be a convenience for getting in and out, but Manhattan unlike any other city you have experienced driving thru. First, there is the traffic getting to NY. Since it is an island there are only 3 Hudson River crossings that deliver you into the city from NJ. On a weekend day it is probably doable but with the Marathon weekend all bets are off. Certainly on a weekday (M-F) I would NEVER attempt to drive into the city anytime before 10 am and I would leave before 3:00pm and be prepared to spend 30-45 minutes in traffic waiting to go thru the tunnel both in and out, weekends included!
Second, there is the tunnel or bridge toll charge of $6.00 for entering (to NYC) drivers.
Third, You may think you can find a parking lot or garage, and you may on a weekend, but be prepared to pay at least $ 30.00 or more Check this site for parkng rates and info: http://nyc.bestparking.com
Because the easiest way from Newark airport to NYC is via RT 78 and the Holland Tunnel this would bring you in on Canal Street in lower Manhattan.
I would select "downtown" or any area south of 23rd street west side as an area to park on the weekend. You can then walk to a subway stop or to a bus stop to take you uptown or hail a cab.
On a weekday, I would seriously think about taking public transport because many if not all parking spaces are leased to regualar commuters and the hourly rate of $ 10+ is usually charged for those willing to pay, if you can find a spot.
Keep in mind most streets are one way to traffic and it can take 20-30 minutes to go a half mile because of the "gridlock" effect of traffic being stuck.
So if you read all this and still want to drive then good luck!
The suggestions in the posts above are all good suggestions and they are made to preserve your sanity and to maximize your time and enjoyment in NYC rather than to spend your time stuck in traffic and worrying about where to park.

I was reminded that there's a bus from the airport terminals to Newark Penn station ($1.35/person) and from there you can get the PATH train to the WTC for $1.50/person.

Thanks so much for the great replies. As far as the hotel, it gets great reviews on Expedia and Tripadvisor. I relied heavily on reviews from these places for my trip to Europe and was never disappointed. I understand that the surrounding area isn't great, but the hotel is clean, looks new, and has a fenced parking lot.

Regarding the driving into the city, I'll take everyone's advice and take public transportation on Sunday and Monday. I have a hair appointment in SOHO/NOHO (Arte Salon on Elizabeth St. near East Houston St.) at 4 pm on Saturday. Would it be okay to drive into the city on Saturday afternoon?

Well - there will be lots of traffic as usual - and you'll have to find a garage to put the car for big $ - and that neighborhood is a little complicated (not on the uptown numbered grid pattern). So - I would stick with public transit if you could.

If you insist on driving into the city on Saturday, then I'd suggest the Holland Tunnel, which is downtown. Just expect to pay about $25 or $30 for parking. On-street parking is basically non-existent in SoHo.

You do not need a car in NYC itself. You can also take the train to 34th street cheap or a bus.

If you drive in, another thing you should check for is street fairs and greenmarkets - finding a detour in advance might save you some time.

I do alot of driving in and out of NY in the summer, and come fall, I am just wiped out - it is mentally exhausting.

Katherine, I'd stay in a dumpster before I'd stay in the area your hotel is in.

It is a scary area.

Check the Comfort Inn in Long Island City. It gets good reviews and is only one or two stops on the subway from Midtown Manhattan.

I've stayed at a number of EWR hotels, overnighting before an outbound flight. Last time, I stayed at the Courtyard, which is right next to the Fairfield Inn. It's an industrial area right by the hotel. You can get into a more dicy area if you drive a little ways. But the hotel itself was perfectly fine, so if you're only going to an from the hotel to sleep (there's nowhere to walk around, or even drive around looking for someplace to eat nearby) it's fine. I assume you would take a hotel shuttle to and from the train station? If so, I don't see it as a problem, other than the distance from Manhattan.

Always remember that the Bronx is up and the Battery is down. That said, I would suggest that you try a little driving right in the heart of NYC. That way you will have stories to tell when you get back home.