Originally Posted by
ijgordon
Obviously staying in Manhattan will cost significantly more.
Perhaps split the difference - there's a Marriott in Downtown Brooklyn that I think is pretty nice. (Though it may not be that much cheaper than Manhattan.) Probably easiest to take a taxi there from LGA, but then you can fairly easily jump on the A train the next afternoon to JFK.
Not sure what staying in Downtown Brooklyn would accomplish. It's not particularly convenient to LGA or JFK. If you're gonna go to Downtown Brooklyn, you might as well go to Manhattan. (Splitting the difference probably means staying in one of the cheesy hotels on the LIE near the Van Wyck!)
BTW, the OP is flying in on a Friday night and out on a Saturday night, for what it's worth.