Are you asking from the point of view of Americans or the rest of the world??
I have spent considerable amounts of time outside of the US both in Europe and South America; and from experience outside the States I would say that the Statue of Liberty is the most symbolic image of the United States around the world.
New York City, as a whole is also an iconic image and I was torn between the two but in the end I believe the Statue of Liberty has the edge.
Now..from our point of view as Americans I think it all depends on where you live and what city/region you identify with the most. No doubt New Yorkers would say the Statue of Liberty while Los Angelinos would say the Hollywood sign.
For me personally....I would say Uncle Sam, but thats just me
