There is No good way easy way from long island pulling a boat. Easiest way is by water..but I know you dont want to do that.
Any way...if your coming from the south shore, Take the Southern State Pkwy. to belt parkway to the Varazzano. SI Xpressway..to Bayonne Bridge..into New Jersey. Follow rt 169 to NJ turnpike. that will put you on at 14a. Go 2 exits pay toll and get off at 14c.
From the North Shore: you could come straight through NYC, but I wouldnt.
Take the GW bridge to the NJ Turnpike South get off at 14 a,b,c, (Neward Bay extension) to exit 14c
Get off at 14c ...at bottom of ramp make left, come under Turnpike, Go around circle 1/2 way bear right . Go straight past Liberty Science center to very end and make right ...you are now in Liberty Sate Park