My advise is to always walk, or drive, around the area at night and make your own decision. Everyone has a different idea of what a "good" area is. You can also call the local police precinct and ask them about problems in the area.
Overall though, as many parts of Jersey City are, that is a transitional area. You will notice abandoned building right next to beautifully restored building. With it's proximity to the PATH it's only a matter of time before all the buildings are restored. In fact, the school that you mentioned at 60 Erie is actually an apartment building that is being converted to condos. The building makes for some nice loft spaces with very high ceilings.
If you have any other questions please do not hesitate to contact me.
RE/MAX Gold Coast Realty
56 Newark Street
Hoboken, NJ 07030
Direct: 201 795-5200 x340
Office: 201 795-0100
Fax: 201 795-1245