Don't think you want to stay in Newark ! :nono5:
I would say that LGA is Much Much Better for you to stay, If you are not staying in the City.
LaGuardia Airport is VERY close to Shea ( you could Almost walk there )
Car rental is right there, or could take a Cab. But might just cost you.
If you do decide to stay around LGA, let me know and I could meet up and have a drink or two. I'm only about 7 miles away