http://naturalizationrecords.com/usa/ should have the addresses you need for those NY petitions.
Also, if George served in the Civil War he may have taken advantage of the special terms involving naturalizations for such soldiers, so be sure and read the MILITARY section at NaturalizationRecords.com to find out how to find those records.
You say you found census records for the family -- You can use census records to help you find immigration and
naturalization years for an ancestor.
The 1900, 1910 ,1920 and 1930 census identify citizenship
status, with notations showing the individual was an Alien,
or had started the Naturalization process or had his final
papers. The year of immigration is also shown. 1920 also
nicely provides a year of naturalization.
There are great clues in the 1870 census too!
If your ancestor has a check mark in the column "Male
Citizens of the
United States of twenty-one years of age and upwards" you
have a clue that naturalization took place before 1870 :-)
To find out what questions were asked on various census
records see
http://allcensusrecords.com/As for passenger lists, all, except NY port, are indexed and on microfilm for the time period you want. You can get a list of film numbers (NARA & FHC) at
http://olivetreegenealogy.com/ships/nara_indexbyport.shtmlScroll down to the state you want and click on the link,
then find the film # you need, then decide whether to order
it in to a nearby FHC or have NARA do a lookup.
The staff of the National Archives will undertake a search
of the original records for a fee.
To find your nearest FHC you can go to
http://www.familysearch.org/Eng/Library/FHC/frameset_fhc.aspTo search NY, use Steve Morse's ONE STEP search engines at
http://www.stevemorse.org/Good luck!