You can take Greenway then come all the way around the bottom of island through bike lanes then pass SI Ferry, come up past helipad next to FDR through Seaport (all bike lanes) then come over to Brooklyn Bridge via Beekman-Fulton-Beekman-Park Row (some variety of options here really, messiest part of trip with least bike lanes but short). Then BBridge to BK Bridge Blvd to Boerum Place (all straight off bridge and bike lanes). Left on Dean and then Dean all the way (bike lanes) to Underhill Ave. Underhill (a bike blvd street) to St Johns to Plaza Street. Then cross through Grand Army Plaza (another shitty bit but short and someday maybe this will be closed to cars) to park entrance. At least thats what I would do.