Branchburg is in western NJ and would be a pretty expensive taxi ride, well over $100. There is no direct public transit to Branchburg however the NJ Transit-Raritan Valley line train stops in Somerville, about 10 miles east of Branchburg. From JFK go to Penn Station by NYAS express bus or LIRR from Jamaica Station via AirTrain. Go to www.njtransit.com and use their handy trip planner using Penn Station as the origin station and Somerville as the destination for schedules and fares. Trains require a transfer at Newark.
Branchburg is in western NJ