There will be 2 of us w/ just one luggage getting in to Newark at about 2:30pm and would like to get to apt on the Upper East side in a reasonable amount of time with little hassle and not an extraordinary expense. What is/are our best options?
Thanks

There is an airport limousine that goes to Grand Central Station. From there you can either take a subway or a taxi.

Well it's not really a limousine, but a bus that stops at either Port Authority bus terminal (west side) or Grand Central (east side) for about $14/person one way. Agree with Michale that from either of those stops, you can either use public transportation or a taxi.

Another option is train into Penn station NYC. More switching, maybe faster, still need either subway or taxi to the apt.

Airlink is a shared minivan service that should give you door to door service for ~$15/person. Here are all the options
http://www.panynj.gov/aviation/egtsfram.htm

Two people to the UES? Definitely take a car service . . .

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Just how big is this luggage?

If it's one gigantic bag for the two of you I wouldn;t try the subway - which has lots of stairs and long passageways - never mind the walk from the subway to the hotel/apartment (you don;t say where it is). (The subway really only works if you have a carry-on you can put on your shoulder - given the stairs, passageways and how crowded the subway cars usually are.)

I would take the shuttle bus to Grand Central and a taxi to UES (total about $45 or so). A cab or car service would be $60+.

You'll wait for the shuttle bus, then you'll stand in line at Grand Central for a taxi (once you've found the exit etc.).

Save yourself a lot of time & aggravation, for little additional cost:

www.dial7.com

NJTransit from Newark to Penn Station, then subway (E to 6). Its very easy, so long as your suitcase is manageable. No tunnels, traffic, delays, etc.