I have found a picture of the Brooklyn Bridge that I would like to use but, I do not know the Artist name.
Photographic images, even ones found randomly on the internet, are copyrighted by the photographer. Legally, you would need to get license or permission from the copyright owner to use it. Otherwise it would be considered intellectual property infringement and you could be sued.
Some images are specifically placed in the public domain. If you do a Google or Yahoo search for "public domain images" you should find some resources and perhaps find an image you like that is free to use.
Would I be better off using my own pics?
Most definitely! Any time you can use your own images or original artwork, you should.
In some cases, however, the content of the image or artwork could still be an issue. I do know that the Empire State Building cannot be used without permission. I don't know about the Brooklyn Bridge, so it may be worth looking into before proceeding.