Having lived in NYC for many years I'd agree that taking a Taxi from JFK to Newark on a Saturday could be very slow and costly. The transit system, however, is quite good. There are a number of rail options:
http://www.panynj.gov/airports/pdf/rail-connections.pdf
Since you have to get to Newark anyway and the trains all require a connection somewhere in Manhattan, you could take one of the trains and see what time you get into the City and play it by ear when deciding whether to emerge from underground and see a few sights.