Bar Majestic
275 grove street, (http://www.barmajestic.com/). cozy, european-inspired wine bar in a restored theater entrance. great date spot. they also have a wine store at the back of the bar, so you can pick up a bottle to take home with you.
LITM
140 newark avenue, (http://www.litm.com/). a trendy bar/lounge, litm which stands for love is the message is a popular watering hole which wouldn't be out of place in chelsea or tribeca. the bar has an assortment of specialty drinks, including martinis, and often showcases a variety of art by local artists.
P.J. Ryan's
172 first street, (http://www.pjryansjc.com/). decent pub, with a reasonable selection of food your typical pub fare, mostly. they occasionally have live music; it's not always good, though.
Zeppelin Hall Biergarten and Restaurant
Located in the new Liberty Harbor development, Zeppelin Hall is a huge biergarten with seating for up to 800 people. One of Jersey City's most popular hang-out spots, with 144 taps and $10 liters of beer. Family-friendly.