I live in and concentrate my real estate business in Weehawken and am aware of more than one professional dog walkers in town. Depending on what if is you are hoping to find in the way of housing , Weehawken may be a very desirable choice . Union city borders Weehawken and so is also serviced by pet sitters / walkers from here in Weehawken . Weehawken had great waterfront parks to run your dog as well.
Anyway if you are not already working with an area realtor I would be happy to try to assist you. Jersey city is also my birthplace so I am familiar with all the communities you mention.