for the city you could always park in the goethals bridge wide load staging lot (off bayway ave.), take a taxi to liberty and then a shuttle into the city. that lot isn't fenced but it is out in the open so i don't think anyone would bother you. i've only parked there long enough to take a nap, so i don't know for sure.
or
call
hudson county motors and see if they would let you park there. it's fenced in and only say @ a mile walk to the secaucus junction train station. exit 15X. they're at the beginning of the industrial park off of seaview, so it's a decent area. you wouldn't have any trouble walking around there in the daytime.