It's probably going to be about $10 cheaper to cab it in from JFK. If you want to see for yourself, take a look at the fare estimator at
http://www.yellowcabnyctaxi.com/, linked at the top of the site. If you don't mind your trip taking about an hour and 20 minutes, you can take the Air Train from JFK to Jamaica for $5 (you pay at the end for the ride for the Air Train), and then take the A train (subway) from Jamaica to Nostrand Ave. for $2.25 (in order to use the subways you have to buy a metro card from one of the automated machines, putting on a minimum of $4.50, you can also do one day unlimited for $8.25) then take the B44 from Fulton St. to Lenox Rd. for another $2.25. To check out directions that are more in depth go to
http://www.hopstop.com/. You can get directions to and from anywhere in the city via public transportation. There's a way to get from La Guardia to Downstate using public transit, but it takes so long it's probably not worth it. But you can just plug it in to hopstop.