I've travelled to New York alone several times from different airports, and I like LaGuardia the best. Newark costs more and doesn't offer an interesting ride. It would be around $20 round-trip if you take Newark, and it's a pretty ugly voyage to Manhattan.
LaGuardia, on the other hand, is cheap (you can take MTA, rather than New Jersey transit), fast, and you get a nice subway voyage through Queens on the 7 train. If you get a Metrocard for your stay in NYC, your LaGuardia-roundtrip could cost as little as $5.
From LaGuardia airport, take the M60 bus to Astoria Boulevard in Queens. Get off here (and you might want to explore Astoria, it's fabulous), climb
up to the subway line above the street, and take the 7 train downtown to Times Square. Then you get to watch Queens roll past you while on the subway!
BlueWizard's blog: The Rambling Corner
HEDWIG: "The road is my home. In reflecting upon the people whom I have come upon in my travels, I cannot help but think of the people who have come upon me."