You can via the Verrazano Narrows bridge.But it may not be cost efficient. The toll is $17 cash or ~ $11.50 using EZ Pass to enter from Brooklyn. No toll going the other way. Depending where you are going, parking once you get there may be difficult as well.If you are planning on going frequently, the ferry to the Staten Island Railway (SIR) to a bus is likely more cost effective but can be time consuming depending where you need to go.The SIR only serves the eastern edge of the island only. Try google maps using the bus option to check out the route / transfers required and estimated time. Note that traffic and missed connections will impact time! You can visit the MTA site for routes. http://web.mta.info/nyct/maps/bu...There are plans being made to address the bus service but nothing has happened yet MTAu2019s Staten Island Bus Overhaul Points the Way Forward for the Rest of NYCNet / net depends how often you need to go and where. If itu2019s frequently, try to find someone traveling the same route to get a sense for time / hassle involved of using public transit.