hi , im trying to find out where my ancestors went to in USA i have the following information_

18 april 1881 arrived in new york
family name woolstercroft (please note that this has been misspelt on the passenger info and should be wolstencroft)

george woolstercroft
wife alice
duaghter anya

george and alice were in their early 20s and george was a coal miner from England - im wondering which city they were living in and the fact that he was a coal miner could leas me to believe he went to the US to work in the the coal mines there

the problem is they had another child born in 1882 but i cannot trace the birth record at all - i would love to find out where they went so is there a possibly link to coal mining records ? ?? lists of workers ect . sadly they missed the census in 1880 and they were back home later on so i dont know where they stayed but would love to know .
could possibly be staying with relatives by the name of Jarvis but thats just a guesss

any info much appreciate