If you want to live in Jersey City, as mentioned, you need to live in a newer luxury building along the river (these building are where I serviced the elevators) and you're definitely not going to find what you want in your price range, at all.
These luxury building are priced similarly to Manhattan. If you want to live in Newark, you better be able to hold your own and have a CCW permit, because you'll need one. I also wouldn't recommend going out at night in either of these areas.
And last time I went to Hoboken was about 3yrs ago to eat a Arthur's Steak House (on Washington Ave) in the afternoon, and the area looked like it totally changed from when I was in my early to late 20's, and definitely not for the better.