Regardless of what you do I'd suggest tracking the flight you're interested in through GF. I've got around 20 setup for various trips, one being your route but in the other direction. Even after purchasing a ticket it's interesting to see the fluctuations in price.
Agree with others you should broaden your search and weigh the options. For your route I usually do
NYC-SFO,SJC,OAK. B6 and UA have sub $200 directs with AS at $209.