I think I'd avoid the Verrazzano just because of the price of the toll. It's like $20 to cross it but only in the Staten Island bound direction so going towards Brooklyn you don't have to pay but coming back you get nailed with a $20 toll.
It is back to two way tolling courtesy of semis shunpiking for good reason. They were using streets of Lower Manhattan to get to NJ creating problems. So they reinstated two way tolling again.
That's good. Hopefully they off set the price of the toll and don't charge $20 in each direction, should be $10 which I still think is too high. Seriously if you live in Staten Island or Brooklyn you should be able to cross the bridge for a lower rate.
It was $19.00 westbound. It’s now $9.50 each way (makes sense). Staten Island residents are eligible for a discount, which was started because they pay a toll every time they return to the island.
Right. When looking at the NYC area tolls, it pays to view them as a system rather than as an individual toll. To cross from west of Hudson (NJ, Rockland county) to east of Hudson (Staten Island, Manhattan, Westchester) you pay a toll, but you don't pay a toll in the reverse (westbound) direction. The southern crossings run by the port authority are the most expensive and then the tolls are cheaper further north. There is at least some toll to be paid to cross the Hudson relatively far north until you reach the Albany area.
The toll crossings that connect the land mass of Long Island (Brooklyn and Queens) to other parts of the city are run by the MTA. These include bridges to the Bronx, two tunnels to Manhattan, and the Verrazano bridge to Staten Island. The Triboro bridge connects Queens to either Bronx or Manhattan. With the change in the tolling on the Verrazano, these are now all $9.50 each way (cash rate, but EZ Pass discounts may apply). So if you are in Brooklyn/Queens and are heading to New Jersey, regardless of whether you travel via Staten Island, Manhattan, or Bronx you pay $9.50 on your first crossing and then the crossing to New Jersey would be free. However, NYC runs 4 bridges between Queens/Brooklyn and Manhattan that are currently free in both directions. So if you instead use a NYC bridge (Queensboro, Williamsburg, Manhattan, Brooklyn), you can go from Brooklyn/Queens to NJ entirely free.
So basically, for travel between NJ and Brooklyn/Queens, unless you use one of the 4 free bridges, you will be paying the same rate regardless of whether you use a combination of Goethals/Verrazano, Lincoln Tunnel/Midtown Tunnel, or George Washington Bridge (GWB)/Triboro (or other equivalent combinations).
And yes, the administrators of the MTA basically allow for a Staten Island resident discount since you must always pay a toll of some kind to return home. Brooklyn residents can still use the free bridges to basically reach anywhere. It may be quicker to use a toll facility, but it isn't strictly necessary.
There are plans to eventually toll the 4 free bridges under a Manhattan congestion pricing scheme for most travelers. This got delayed due to coronavirus. Based on my understanding of the proposed plan, you can still cross the bridges for free so long as you don't enter the surface streets of Manhattan below 59th street. So you can cross the Brooklyn Bridge and reach FDR drive (a parkway) for free as long as you don't exit in lower Manhattan, and you can cross the Queensboro Bridge for free so long as you only drive to the north of 59th when you land in Manhattan. But the Manhattan Bridge and Williamsburg Bridge empty out onto streets so those crossing would be subject to congestion pricing.
The main purpose of congestion pricing is to raise revenue, but I beleive a secondary purpose would be to allow crossings that avoid the Manhattan CBD to be cheaper. So driving from Brooklyn to NJ would be cheaper via Staten Island (or Bronx) than via Manhattan surface streets to reach the Holland or Lincoln Tunnels. Presumably, it would still be free if you use the Brooklyn Bridge to the FDR Drive to the GWB or the Queensboro Bridge and drive north on some Upper East side surface streets to the FDR to the GWB.