How long are you going to be gone? I always drive to JFK and will do so again when I go to Chile for two weeks in February. I park at a non-airport off-site facility (That reminds me to make reservations!) and have been pleased with the service. Never a wait of more that 5 minutes to get shuttled to the terminal. Besides, it seems cheaper than going any other way.
If you do not have a car you could take the train from Hartford. The schedule my be more precise but will take much longer.
By the way, I live in Essex, so it is about a 2 to 2.5 hour drive.