Is there one (or more) organization that has all the information of
all New York City or USA companies/organizations that are
incorporated? (Is it possible to know where a company/organization is
incorporated?).

I believe this site may be of use to you especially if you're trying
to avoid "Name Conflicts".
http://dnb.com/us/

Do similar (free) sites exist?

Thank you for your patronage and rating.
Unfortunately, I could not find similar (free) sites.

I did come across http://www.hoovers.com 
for easier  company lookup.

Thanks.
If you come across similar (free) sites in the future, please post it
here.(Besides D&B & Hoover's (D&B is buying Hoover's now) - there
aren't similar companies? D&B-Hoover's has a monopoly?).