Journal Square isn't that bad, however if you want a perfectly safe neighborhood in JC you need to keep it to the east of the Turnpike and to the south of the Holland Tunnel. This is the area around the Exchange place and Grove St stations. Of course these areas are much more pricey than Journal square.
Lots of different people live in the journal square area. Jersey City is a very multi-racial city. Lots of Phillipinos, Indians, Blacks, Hispanics, & Whites live around Journal Square. Its not a perfectly safe area, but isn't too bad by JC standards. I would be less concerned with violent crime and more concerned with my car being stolen off the street if I lived in that neighborhood (as this is quite commonplace in this area of NJ). The car thefts are common because lots of gangs (and probably the mob as well) run rackets where they steal cars and drive them over to Port Newark so that they are shipped out of the country to Latin America and Europe.
The town of Harrison (one stop and 10 minutes) farther down the PATH line is pretty nice. Perfectly safe town even though it is right next to Newark. Lots of different people live in Harrison, whites, Asians, hispanics, and the Portuguese. The largest Portuguese/Brazilian neighborhood is right next door to Harrison in the Ironbound section of Newark. The Ironbound is also a pretty decent neighborhood but is not too welcoming to people who don't speak Portuguese.