Hoboken rent is pretty outrageous, even with a roommate. Jersey City isn't as bad, but there are certain areas where the rent is just as bad as Hoboken.
As for neighboring towns of Newark that are perfectly safe and you don't have to worry about - Bloomfield, Belleville, Nutley, Clifton. Towns across the Passaic river (but still extremely easy to get to Rutgers Newark from) - Kearny, North Arlington, Lyndhurst. All have reasonable rent unlike Hoboken and parts of Jersey City.
78 runs at the southern end of Newark, so those towns.. Union (which is a bit more urban than the following towns, but not like Newark), Springfield, New Providnce, Berkeley Heights, Scotch Plains.
These towns are a lot more "town'ish" than those I listed above. Every town I've listed is perfectly safe to live in, but the ones off 78 are more suburban, I suppose.
I don't know how much I'd recommend towns off of 78. I mean, they are nice and perfectly fine, but the morning commute, anywhere in North Jersey, is really terrible. Which is why I recommend any of the towns I listed earlier, as they're all local, and you don't even need to get on a highway to get to Newark, unless you wanted to.