[StatenIsland]

Can somebody tell me why public polling is not illegal?

The First Amendment.

Then why can I not campaign right outside the voting booth? It is an unfair attempt to manipulate the outcome of an election, and trumps my right to free speech.

[woodb01]

You can engage in “electioneering” within up to around 50 feet of most polling places. That means they have signs, and can distribute literature, even while you are in line until you come to within 50 feet of the voting booth.

[nwrep]

Then why can I not campaign right outside the voting booth? It is an unfair attempt to manipulate the outcome of an election, and trumps my right to free speech.

Ah yes, the straw man argument. Well, the First Amendment has many exclusions and restrictions. Yelling "fire" in a crowded theater is one, canvassing/campaigning within a 100 feet of a polling station is another. In the case of both, the balance is between your right and the hardship imposed on others due to you exercizing your right. In each case, the balance is resolved in a common sense manner.