Baden is not 30 km from Bremen -- it is several hundred kilometres away, if you are referring to the Duchy of Baden (today's state of Baden-Wurttemberg):
I did find a naturalization record dated June 7, 1899 in New York for a Johann F. Reck, aged 44, cigar maker, arrived in New York on November 13, 1875. The full naturalization record should provide more information, as should his church marriage record to Rose.
1900 US Census
Manhattan, New York
(note that Fritz is a popular nickname for Friedrich)
Reck, Fritz, Head, born January 1856, aged 44, married, 24 years, born Germany, parents b. same, immigrated 1875, sigarmaker (sic)
Reck, Rosa, Wife, born March 1853, aged 47, married, 24 years, 11 children born, 7 children living, b. Switzerland, parents b. same, immigrated 1876
Reck, Rosa, daughter, born February 1878, aged 22, single, b. New York
Reck, Fred, Son, born August 1879, aged 20, single, b. New York
Reck, Morris, Son, born October 1881, aged 18, b. New York
Reck, Charles, Son, born October 1887, aged 12, b. NY
Reck, Frieda, Daughter, born May 1889, aged 11, b. NY
Reck, Elsie, Daughter, born May 1890, aged 10, b. NY
Reck, Albert, Son, born October 1895, aged 4, b. NY
In the 1892 New York State Census, they are living in Ward 4, Long Island City, Queens County, New York. He seems to have used the name Frederick (properly Friedrich), rather than Johann, which was often the case.The 1905 New York State census, Fritz and Rose are living in the Bronx. In 1910, they are living in Brooklyn.If he died in Newark, Ohio, they only lived there for a short period of time. Rose is living in Licking County, Ohio, in the 1920 census.
Frederick's death index record (familysearch.org) gives his birth date as 3 January 1855, died 26 February 1914, aged 59 years, 1 month, 23 days. His father is named as Frederick; mother's name is not given.