I was born & raised and still live in Jersey City, NJ. It's an urban city (although up until the early 1920's it wasn't).
People talk about JC as though it were the gum on their shoe. But I'll tell you something. I don't see myself leaving here anytime soon. My husband and I just bought a condo here a few months back. I like JC very much. I like that fact that JC for the most part is very
diverse. I like the fact that if I choose not to drive, there is public transportation to just about every point in the city and we are a stone's throw away from NYC. I like the fact that if I want to go to McDonald's at 1 am, it's still open. Most people in JC are friendly, others are not so friendly. But hey, that's anywhere you go.
I understand your feelings about schools. However, I disagree with the "ghetto" comment. I attended both private & public and I attended pretty good schools in areas of JC considered "ghetto". My former alma mater has been ranked one of the top, if not the top high school in New Jersey and in the US for many years and it's located right in JC (McNair Academic High School). I will also mention that I am a teacher and I will say that school location has little to do with the actual education you receive.
Threesmom, you mentioned that your town has similar problems with that of an urban area. Those things will not go away by moving to a suburban town. They may be kept under wraps better because of money and politics, but they won't go away.
I know you are concerened about your children and their well being and as parent, you very well should be. I suggest that you and your husband both make an individual list of pros and cons of why you want to move out of NJ, compare the lists, and then make another list from what you both consider to be the most important reasons for leaving.
Whatever your decision, I wish you luck!