Transportation from Upper East Side to Newark International

I like to use Rome2Rio to get a quick overview of multiple transportation options between two points, whether within a city or across the world. By default it will display results broken down by mode of transportation, and for each mode, showing the estimated time and cost. For each mode, you can click on it to get more details such as the exact routes and schedules and pricing information.

From the search results we can see that, excluding driving yourself, the cheapest option is public transportation, expecting to take a bit over an hour to get there. If you're in a hurry you can take an airport shuttle for quite a bit more than that, but since I know how traffic is in Manhattan, I would take the 22 minute estimate with a huge rock of salt.

So the usual tradeoffs people have to make getting to and from an airport are time, cost, and the need to carry a lot of baggage. If you have more than one checked bag per person, it's probably best to get an airport shuttle even if it's more expensive, as moving that baggage around the subway or a NJ Transit train would be unwieldy at best. If you're traveling in the middle of the night and the tunnel isn't under construction or something, then maybe that can be done in 22 minutes and you can trade off the cost for time if you really need to. Otherwise if you have no more than one checked bag and one carry on per person, you can probably just take public transit with little difficulty.

Note: This answer specifically refers to public transportation options, as it is assumed by default that Manhattan traffic + Lincoln Tunnel traffic will be horrendous. As noted by phoog in the comments, airport shuttles and taxis will likely be faster than public transportation when traffic is low.

From 78/2nd to Newark, the most effective way to go by public transportation is to take the (Q) from either 72 St or 86 St stations (depending on which is closer) to 34 St - Herald Square. From there, walk west to Penn Station to access New Jersey Transit. Alternatively, you could transfer to a 1/2/3 train at Times Square and then go one station south to Penn Station but the transfer corridor is circuitous and definitely less convenient than walking from Herald Square.

Service to Newark Airport is provided by the Northeast Corridor and North Jersey Coast Lines. The Northeast Corridor (the more frequent one) timetable can be found here: https://www.njtransit.com/pdf/rail/R0070.pdf

For the NJ Transit trip planner, it's available on the NJ Transit website

Once you're on a NJ Transit train for Newark Airport, the ride shouldn't be more than 25 minutes.

At the airport, you will then need to take the AirTrain to your terminal.