What is the least expensive and easiest way to travel to the Sheraton Manhatten from either Newark, JFK, or LGA. I havent booked the tickets for July 5th trip yet. There are 4 of us each with 1 pc luggage.

The least expensive way is NEVER the easiest. For 4 people from any of the airports, you might just as well take a taxi or car service.
dial7.com is a good car service. You can get to the hotel from JFK for as little as $7/person, but it requires lugging baggage up and down stairs. A taxi will cost $60 total, shared by 4 is a pittance.

Of the three airports, Laguardia is the closest to the city. So, obviously, the cab or car service cost would be the least of the three.
And, with four of you, that's the recommended way to do it.

Agree with 4 and luggage the only sensible things are:

LGA - Cab to city - about $35 or so

JFK CAb to city - $45 flat fare plus tip and toll for abuot $60

EWR - Car servie (look at web sites of CArmela nd Dial 7 for coupons) - also about $60 - but you will know in advance - and you have to pay toll in addition to the fare

With 4 people, you won't save money by using airport buses or trains over taxi or car service.

Only way to really save money is by using local buses. From LGA, M60 takes you to Manhattan, then switch to another bus or subway. From EWR and JFK, using local buses will take a while and require multiple switches.

The airport bus to manhattan from newark is $15 one way, so definitelay not a savings over car service or taxi (I think a taxi from EWR to NYC is about $50 + tip and tolls). As already mentioend, car services is definitely in the same ballpark as taxis.

Book a car service with Carmel limo
http://www.carmellimo.com/Airports.shtml

They often have discount coupons on their website.

You can in fact take various local city buses and trains to get into the city - but

It will take a long time - 1.5 to 2 hours or even more - since some run only every 30 minutes or so

You will have to make several changes, possibly involving dragging your luggage up or downstairs

You will be on local transit often packed with local commuters - and no place to store sizable luggage

I would reco this option only to a college student with no $ and only a shoulder carry-on.

Thank you. I know Least Expensive is never easy, however If I saved over 100.00 per ticket, it will be worthwhile. I appreciate all the advice. Hopefully I will book my tickets tonight... Again, Thank you