Renting a car in DC and after a week @ Jersey Shore will end our trip in NYC.
Prefer not to drive all the way into Manhattan.

Is there someplace to drop the rental and catch the train into the city?

Why don't you check with whomever you are renting? Or simply go on-line and look where are there are facilities.

You can check on NJ Transit and The Path.

The major rental car companies have facilities downtown which would make it convenient form the Holland Tunnel.

Which rental company are you using? And where at the Shore will you be? I live at the Shore and the major car rental companies have rental facilities near me. The NJ Transit Coast Line runs along the Shore to Bay Head.

Downtown Newark
Newport
Hoboken
there's a Hertz at Central Parking in the Harborside (Mack-Cali) building one block from Exchange Place PATH station. It's on Columbus and Greene.

Jersey City has Budget Car Rental at the Grove STreet Station.

IMHO by the time you've come to the nearest parts of Jersey - right across from the city - you've already had to fight a lot of traffic.

I would either get on a train much earlier or just drive into Manhattan and avoid a lot of foofing around in the most crowded and confusing parts of NJ.

Something to check, as it may work, or it may not:

Rental car companies MUCH prefer to have lots of cars at airports instead of city centers. Thus, they will often give a real bargain if you pick up a car in a city and return it to an airport. For instance, the rental company might waive the drop off charges -- in effect, they're paying YOU to drive their car back to an airport. I've done this a couple of times and the reduction in cost has sometimes been dramatic.

You'll still have to get from the airport into Manhattan but, if the cost to rent the car is reduced enough, you MIGHT actually come out ahead.

Also consider dropping off all luggage and everybody but the driver at a rail station, allow them to ride the train into Manhattan, return the car to the airport, and then have the driver easily ride (even a city bus) to re-unite with everyone else at the Manhattan hotel.

We're staying at Times Square.
Probably driving from Ocean City or Cape May.

For those familiar:
1. Drive into the city & return rental after dropping family off at the hotel OR
2. Drop car at Newark airport & ride train to Penn Station.

I'm willing to pay a little premium for convenience/ease.
No problem with city driving, just wondering how big of a hassle it will be vs ditching the car earlier.

If you are staying in Times Square, then drop your car at Newark airport. That's by far the easiest solution. From there you have very good train and bus connections into Manhattan. And you will avoid the expensive tolls into Manhattan as well.

If you drop it at Newark you can take the car rental shuttle back to the airport and there pick the large airporter bus (NOT supershuttle) which you can get to Port Authority bus Terminal - only a couple of blocks to Times Square (IMHO easier than taking Air Train, then NJ TRansit train to Penn Station NYC, then the subway - hauling your luggage all the way to get to Times Square.)

@nytraveler: Sounds like a good plan. Our hotel is a block from the Port Authority.

Still advise this if during rush hour? Guessing traffic INTO the city will be better than leaving @ 5-6PM.

I know many people shudder at the thought of driving into the city, but if time means anything, simply dropping the car off in midtown will likely be less complicated and quicker than most of these suggestions of various kinds of logistics. Personally, I think some of the navigating around Newark Airport, then the various connections is both more complicated and more time consuming than simply dropping the car off in the city, particularly if it's near your hotel.

Agree that the fastest is just to drop it at an office near your hotel - or drop the passengers and luggage at the hotel and then drop the car at a rental office. Obviously exactly how close to the hotel depends on the agency - but the majors have offices all over the city.

The Lincoln Tunnel into Manhattan during rush hour is no picnic. I'd take the train and save at least 30 minutes, even though you come into Penn Station. But coming closer to the Port Authority is tempting. Just prepare for a slow trip.

I'd be the first to agree with Doug's assessment of the Lincoln Tunnel IF you are arriving into the city at rush hours weekdays, but if you are arriving Saturday or Sunday or between the hours of say 10 AM and 3 PM weekdays, I really don't see you saving 30 minutes but probably adding at least that much by doing the "double transportation" thing.

The locations in Jersey City ClarkGriswold mentions put you closer to Manhattan than Newark airport does. There are PATH trains and ferries between Jersey City and Manhattan.

There are some nice places to stop between Washington and Cape May and Jersey Shore and NYC if you're interested. Winterthur Estate in DE and Longwood Gardens and The Grounds For Scuplture near Trenton, NJ.