The Staten Island Ferry is a free ferry ride into NYC. It also passes the Statue of Liberty! :) Recommend buying a Metro Card > taking the Staten Island train to its final stop aka the St. George ferry terminal (you only need the card to get off at St. George) > Hop onto the ferry > boom you’re in NYC!
I'll admit...it's not the MOST thrilling but there is a dine in movie theater, restaurants, Dave & Busters, etc.
The Staten Island boardwalk goes along the beachy SI coast! Nice for a summer day. Plus a clear view of the Verrazano Bridge...as a Staten Islander uhh - just, dont go in the water. (Don't ask).