We live on Long Island and our choice is the George Washington Bridge to the Throgs Neck Bridge then follow I295 to I95 (the LIE). Going the Veranzano Bridge route means taking the Outerbridge or Goethels bridges to Staten Island. Both bridges have extremely narrow lanes - our friends refer to it as the "OMG" bridge. No time is especially risk free in terms of traffic at the GW and cross Bronx. We usually aim for hitting the GW and Cross Bronx expy at mid day. Depending on where on LI you plan to go, try to be at your destination by 3 or so since rush hour traffic builds after 3. We usually pick a campground not too far from the bridge and stay there the night before, then head out 10ish. Happy to provide any other information you might need.