Have you attempted to find a naturalization application for this individual? That document can contain specifics about where the person originated from, and other information.
Before attempting to jump the pond, exhausting all records on the US side is a good idea.
The US census records hold all sorts of clues to narrow down time and location of events. Reconstructing the entire family, not just your direct ancestor, can also lead to time and location of events.
Knowing where the eldest child was born and baptized can lead to the location of the marriage. In the case of finding a marriage location you follow the whereabouts of the bride and her family.
Posting information on the boards may help others and you in search.