there are two walkways across the bridge. one on the north side mostly open during weekdays (it has stairs and is a pain) and one on the south side which is open usually on friday, saturday, and sunday. this changes based on the constellation of the stars it seems. no idea why that is.

you can check ahead which one is open here:
http://www.panynj.gov/CommutingTrave...#gwb_sidewalks

i'm not sure about parking (i bike over from brooklyn. no car needed). i see a lot of people unload their bikes and leaving their cars behind along the east side of hudson terrace.

these are the entrances: