The NY Airporter is a mistake -- a waste of time and money. I fly out of LGA often as I am from NYC. If you want the cheapest & easiest, take the M70 bus to the 7 train which takes you to Times Sq. Lightyears faster than the NY Airporter tomorrow afternoon.
It is very easy to take the bus and subway to Times Sq. If you're landing at Terminals B, C, or D, take the M70 bus just one stop to Broadway/74th St subway station in Jackson Heights; it's huge. You can get a metrocard for the bus & subway at the ticket machines by the baggage carousel at LGA. The M70 is on the honor system so with the metrocard at the bus stop, use your metrocard at the SBS machine at the bus stop to get a white ticket. Hold on to it. When you arrive at the Broadway/74th, use your metrocard at the turnstiles and take the 7 train which is the only elevated subway at that station. It is a FREE transfer.
Total cost: $3.75 which is the $2.75 fare + the $1 fee for the metrocard. This is also the FASTEST way into town because the Airporter will sit in bumper-to-bumper traffic on the roads in Queens, on the bridge heading into Manhattan and then be in bumper-to-bumper traffic in Manhattan all the way to Times Sq. Why pay $15 for that headache???
Terminal A at LGA is the Marine Air Terminal; it's used for the Delta Shuttle from Chicago & DC.