Safest New Jersey city nearest NYC by public transportation? (future law student)

I would definitely try Hoboken. You can be in the city within 10 minutes by Path and depending on where your apartment is located you're always within walking distance of the bus or train. I take a bus four blocks away from my apartment and I'm at Port Authority in 12 minutes. it's a very safe town full of young people and families. It's expensive but probably less so than Brooklyn or the other boroughs. Give it a try!