The Amakusa Christian Museum is actually up a hill within the town of Hondo (modern "Amakusa" is a union of several earlier residential areas), and not in Amakusa City proper. I believe it might be about a 30-min. cab ride. But if you are not staying in Hondo, it would be best to figure out how you can catch a taxi for a return ride (e.g., with a cell phone call). Hondo does not have taxis cruising even the main streets; it was hard enough to find the little main bus station. I was at the museum in the late morning in late March; the cafe was not in operation. So you should inform yourself--but there are many places to lunch down in the town (in Hondo). It's a nice walk down. I don't know what bridges you are referring to. The series of five bridges is not on Shimoshima Island, where Amakusa City proper is. I think they are the bridges between the main part of Kyushu (coming south from Kumamoto City) and Ueshima, the island above Shimoshima. The whole area is beautiful, however.