If you guys do go to Bayonne to look at the car, stop in at Big Apple Pizza on Broadway and about 19th street. Super thin crust pies. An absolute classic.
The Blimpie base on 25th Street is exceptional too. The owner upgraded the cold cuts to Boars Head and Thumann's.
I don't think there was a crazy amount of flooding in Bayonne, not nearly like Staten Island or the shore towns, but it is worth checking out.