If the dogs need a lot of space, look at communipaw and light rail into downtown JC (assuming that’s where the office is). Liberty state park is a true gem (and under utilized)! Get a car.

Other than that, I’ve moved cross country three times (I know that that’s different than abroad), but corporate owned apartment buildings were a godsend because 1) you can rent sight unseen and 2) they have dedicated staff to deal with the admin details. There are plenty of new buildings in downtown to choose from. Many parks to walk to although I have never seen so many lawless pet owners that don’t pick up after their dog. It’s so out of hand. Good luck!