I just did a little research (very quickly) with the Ancestry census records.
In the 1885 Territorial Census and the 1900 Federal Census, it appears there was an Andrew Bradley born about 1834/5 in New York. Looks like his wife Martha had 2 children a William and another child that didn't survive. Martha and William were also born in New York. They appear in the Moody county census, which would be just down the road. Brookings was and is still the major hub city for a large portion of Moody county.
There are several records for "James Monroe", though they were born in a variety of locations including Kansas, Iowa, Canada, Massachussettes and Illinois.
I'll let you know if we discover any other details!