So... asking me isnt going to give you an objective answer as I will always go up to bat for Urban NY and NJ, I just think the neighborhoods in that collection of cities and boroughs (especially the ones with 24/7 train access) is just hands down offer the best value in the region.

With that said, I would caution against Elizabeth, not because its a bad city (its pretty fun) its just difficult to get in and out of if you are relying on public transit and want to access the rest of the urban core since the city is only connected to Newark and NYC by NJ Transit.

I would advise picking Harrison, along the path, as its super quiet to give you a more suburban lifestyle, while having 24/7 Path access to Newark/JC/Hoboken/ and 4 of the 5 boroughs. It would make it much more doable to get into Manhattan for a night out/make it easier for you if you decide you want to venture out into Queens or Brooklyn for a night out as you wont be stranded past midnight (just need to either plan ahead of time to make sure you connect easily without a huge wait or prepare for a 20 plus minute wait once you get to a path station). JC is definitely expensive, but as long as you live along the path, you can access JC and beyond without much of a hassle for about half the price.

To make a long story short, I do think moving closer will be best. Even if you arent in the center center of the action (living in manhattan south of 96th Street) so long as you have 24/7 train access you are literally living in the center of the action and can access some great neighborhoods for fun as well if you want to explore outside of your neighborhood