Here are some suggestions we think you might enjoy while visiting The Garden State which is right across the pond from New York City. 
Fun Facts:
1. New Jersey is home to more diners than any other state. 
2. The most famous street and the main artery of New York is Fifth Avenue and the most visited place in New York is Times Square. 

HUDSON & CO BAR AND GRILL

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Stylish gastropub featuring elevated American fare, cocktails & a patio with river vistas.
*Outdoor seating
*Good for watching sports
*Kids menu

RPM Raceway

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America's ultimate all-electric indoor karting and entertainment destination providing an authentic, exhilarating and safe racing experience second only to climbing into an actual race car.

HUDSON LANES BOWLING ALLEY

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This long-standing bowling alley has 60 lanes plus a pro shop, a bar/lounge & party rooms.
Service options: Serves food
1 Garfield Ave, Jersey City, NJ 07305
Fridays: 1:00pm-11:00pm
Saturdays: 10:00am-11:00pm

BARCADE

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Barcade is a combination bar and arcade with a focus on classic video games and American craft beer.
*Has outdoor seating
 *Serves great cocktails 
163 Newark Ave, Jersey City, NJ 07302
Menu: barcade.com
Friday – Saturday: 12pm – 1am

HUDSON RIVER WATERFRONT WALKWAY

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The Hudson River Waterfront Walkway is a promenade along the Hudson Waterfront in New Jersey.  The Waterfront offers Manhattan views of the New York City skyline and is one of the best ways to soak up the city.
Note:  This site links to other things to do.
Address: Hudson River Waterfront Walkway, Jersey City, NJ 07310
Hudson River Waterfront Walkway is a 5 mins drive from Residence Inn by Marriott Jersey City or Canopy by Hilton, Jerry City.

MILOS-NYC HUDSON YARDS

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MILOS at NYC - Hudson Yards 
20 Hudson Yards, Fifth Floor
New York, New York 10001
Hudson Yards is west of Times Square and offers the matchless seafood of Milos served high up, with unrivaled views of the spectacular sunsets that illuminate the Hudson River. The stunning new Hudson Yards location features views of sky and river, presented in hues of blue that shift as the hours go by.

THE EDGE-NYC HUDSON YARDS

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The Edge - 30 Hudson Yards, NYC
The Edge is the highest outdoor sky deck in the Western Hemisphere.  It's suspended in mid-air, giving you the feeling of floating in the sky with 360-degree views of Manhattan skyline you can't get anywhere else.
PATH (Train)
https://www.panynj.gov/path/en/index.html
PATH transports between New Jersey 
and New York
Hudson Bergen Light Rail / Bus
njtransit.com
NY Waterway Ferry
nywaterway.com

FYI
The best way to get from Jersey City to NYC is with the PATH Train. Although there are bus and ferry options, the quickest way is to take the PATH that runs along Exchange Place, Grove Street, and Journal Square.
American Dream
1 American Dream Way
East Rutherford, NJ 07073
Phone: (833) 263-7326
americandream.com
(16.7 miles from Jersey City)

Newport Plaza
125 18th St, Jersey City, NJ 07310
Phone: (201) 626-2078
https://www.simon.com/mall/newport-plaza

Newport Centre
30 Mall Dr W, Jersey City, NJ 07310
Phone: (201) 626-2025
https://www.simon.com/mall/newport-centre/stores