You can park along First Ave. overnight and be ok. It's an industrial area but there are a lot of people working overnights. There is a Costco by 39th street that you can park in the parking lot too. They won't bother you. Just be out by 8 am.
Im not saying you should do it. But Seafrigo Cold storage in Elizabeth has overnight parking for folks picking up or delivering there, and there is no guard in the guard shack. If you're pulling a reefer you look the part and probably won't be bothered. I've slept there three times and only picked up their once.