Actually, there is construction work being done on the A line on weekends. What this means is, you take the free shuttle bus to the Howard Beach station, where you have to change to the (free) MTA bus which takes you to the Rockaway Blvd station where you then can take the A train. It's still cheap, but takes at least an extra 45 minutes.
I second rssrsvp's suggestion. Take a cab from JFK to your hotel near LGA. You should try to see something of NYC if you have the time. Your hotel near LGA could keep your luggage for you while you see the sights. And public transport is also easy from LGA. There is the M60 bus($1.50), from which you can transfer to practically all the subway lines(N,6,1,2,3) at no extra cost). It stops at all the terminals at the same place the Q33 & the Q48 do(basically at the center of the loading area).

Edited for grammer


[This message has been edited by SeeYa (edited 12-12-2001).]