I would say, from JFK the 45$ flat rate cab is for me at least the best option.(you can make it cheaper with a pair up) the Airtran to the lower city, then subway connection can take a LONG time, well over 1:20 sometimes longer depending on connection times. It also can take a long time to get to the JFK terminal depending on which airline one flies in to.

From LGA cabs for me to IC Barkley tend to be about 30$,

The fastest and cheapest option is the airtran from EWR (newark) to PENN, and from there it wouldn't be more than a 5$ cab ride to the new IC.