Barbara (and anyone else interested),
I've been to Hoboken Cemetery in the last 2 years and can say that while the front half of the cemetery was maintained well enough with grass cut, etc. the back half on the hills above the receiving vaults was a treacherous jungle of plant growth (especially poison ivy) and is populated by gophers and their dangerous holes. I went in May but I'd suggest going maybe in the Fall to early winter when a lot of the underbrush should have died off (provided there is no snow!) Although I felt secure enough in the front portion near the main gates, I never saw another person coming or going and would not venture into the back alone. There did not seem to be anyone at the house at the gates of the cemetery or any groundskeeping staff on site.
As far as records, the cemetery and its records are currently maintained by Epstein Management and you can write, email or call them to check if a person you think is buried there. They were very helpful to me and though they never reply to emails, within a day or two of sending in inquiry, they had mailed me a photocopied plot map with the location of the graves I requested. They did not ask for any money. As long as you don't drive them crazy with tons of lookups they probably wouldn't charge you. Here's the contact info:
Epstein Management Corp.
PO Box 222 / 731 Kenilworth Avenue
Kenilworth, NJ 07033-0222