Apartments For Rent Beacon Jersey City . This apartment community was built in 2013, renovated in. Check rates, compare amenities and find your next rental on apartments.com. Incredibly Charming Heights Rental has Bright Rooms, Oversized Living from jerseydigs.com A maximum of 2 cats are allowed per unit. The beacon is a neighborhood located in jersey city, new jersey. The beacon apartments is located in jersey city, new jersey in the 07304 zip code.