Betseylee is correct. You need a clue from something, an old letter, a baptismal record, the immigration record of a relative who came much later. Here's a clue: any chance your ancestors did work related to mining? Seems to me that's an industry in Ohio. If so, they could have come from the Kutna Hora area in Bohemia, or the city in northern Moravia which had a lot of mining. I forget the name -- started with an "O", I think. There are some other mining locations, too.
Don't take the "Bohemia" designation too literally; frequently Moravians simply said Bohemia because it was easier than trying to explain Moravia.
Ship's records in 1871 rarely had the home village listed. Now, in the late 1890s forward, yes. That's why I said, if a relative came over later, research them, and you might find a clue. But you also need to find the ship's record manifest and look at all the people listed on the same page with your great grandparents. Chances are, if they are also from "Bohemia", they might have come from the same area. So you check around in Ancestry to see if anyone has a family tree on those folks.
Church records. I know that you can get records from a Catholic archives in Ohio for a modest fee. I don't remember which diocese it was; it's been about 6 years since I did that. They won't make a copy of the exact record, but will issue an official certificate. They do a pretty good job of transcribing the text in the parish books. So it looks like your great grandparents were young enough in 1871 (21 and 18) that they probably had some children over here. If you have birth dates, you can contact the rchives in Ohio. Look on the Web for info.
Good luck. Sometimes it is just that when you stumble on to something. Then you have to wonder if the ancestors had a hand in your "luck". We have a saying: "They want to be found."