Here's a description of how they work (complete with pictures):

<link>

Putting these along Broadway might smooth out the traffic a bit.

Personally, I think roundabouts are okay, but introducing them into an already developed "traffic culture" can be problematic. One was introduced in Lexington, KY (whose traffic of course can't begin to compare to NYC's), and drivers reacted like chimps at their first fire. It is generally avoided in favor of alternate roads. (But that too may bring about the desired effect!)

With 356,000 pedestrians going through Times Square every day a roundabout would never work. Cars, legally having to yield to pedestrians in crosswalks, would never get enough gaps in pedestrian traffic to smoothly enter or exit the roundabout.