The Independent is very cool. It is definitely geared more toward the new young professional crowd that is moving into Union Square. It is both an upscale restaurant and a bar. The food is somewhat "fancy" and so if you are in the mood for fancier food, this might be the place for you.
In recent months, perhaps due to waning interest in the Independent, they have instituted a couple of nights per week with gimmicky kinds of themes to draw crowds, and it seems to be working. On Monday nights, they host an amature poker night (Texas Hold'Em). No money is exchanged (and there is no fee to enter) and the winner of the tournament receives a small prize. It is tons of fun and it feels like the whole neighborhood comes out for it. Each week, there are more people in attendance. Tuesday nights they show a free movie that fits in with their monthly movie night theme. The movies are usually pretty good picks. We went one night when they were showing "This is Spinal Tap". You get a bag of free popcorn at the movie night.
I highly recommend stopping by - it is a fun little place!