The symbol of NY

When I return to Brazil, I'll share with my students the expectation that I had to know the great symbol of the USA and certainly the greatest symbol of NY.
Unfortunately for me it wasn't possible to see close (I think that tourists should have the right to go up to it, even during periods of reform, because not go through there is a frustrating experience). It's the same when someone visit the Rio de Janeiro and not go until the Monument of Christ the Redeemer or go to Manaus and not go to the Amazon Theater.
I went there twice. First I went to the Statue Liberty Park in New Jersey but the access bridge was banned, another time I went by boat but can't stop it.
I believe that everyone coming to NY wishes to visit the Statue of Liberty.