I don't find a car necessary in downtown. I don't have a dog though.

I do a mixture of Amazon Fresh, Amazon subscription, and Target delivery for grocery staples. For last-minute or stuff where I want to pick it out there are enough walkable places (Oliva, Key Foods), which aren't cheap but fine if you're not stocking up. I guess you can walk to ShopRite too. Super Buy Rite has free local delivery for beer/wine/liquor and good prices.

A lot of it comes down to whether you want/need to be in suburban NJ frequently. Car rental is fine for a weekend trip now and then, but probably not if you're visiting your parents in Morristown every weekend. A lot of the people without cars have social lives more oriented around either JC itself, or JC+NYC.