You can't bike on the Verrazano-Narrows Bridge. They were going to build a pedestrian-bike lane, but the winds are always at gale force there because of proximity to the ocean and the effect of the narrows. You can't bike on the other bridges or tunnels either. The only bridge that you can bike to Jersey on is the George Washington, built before they thought of limiting access to NJ/NY. There are a fair number of days that you can't even use that on a bike or walking because of hazardous conditions.
Interestingly, the Port Authority of NY/NJ is presided over by the governors of their respective states. When was the last time a governor thought of revenues as a local matter? I'm sure it's okay not to pay tolls on I-90 for any NYC projects, but we should always fork over our cash for the benefit ofthe stateUPstate. That's just jim-dandy.